{"meta":{"query_hash":"aeedc73d34ad","filters":{"venue":"International Journal of Number Theory"},"cohort_total":200,"direct_labels_cover":0,"predictions_cover":200,"exported":200,"export_cap":100000,"truncated":false,"label_status":"direct model label, unvalidated","prediction_status":"machine_predicted_unvalidated (Codex and Gemma teacher distillation)","score_status":"score_only:v0-immature-baseline","snapshot":{"source":"OpenAlex, pinned release, all 482 partitions","release":"2026-06-24","frame_built":"2026-07-12"},"permalink":"https://metacan.xera.ac/q/aeedc73d34ad","api":"https://metacan.xera.ac/api/v1/cohort?venue=International+Journal+of+Number+Theory"},"results":[{"id":"W1201167659","doi":"10.1142/s1793042115500165","title":"A remark on the 𝔐<sub>H</sub>(G)-conjecture and Akashi series","year":2014,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Multiplicative function; Dual (grammatical number); Series (stratigraphy); Prime (order theory); Elliptic curve; Reduction (mathematics); Group (periodic table)","score_opus":0.013336628944455238,"score_gpt":0.2653587523479674,"score_spread":0.25202212340351215,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1201167659","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9727373,0.000048071106,0.0018903363,0.0042198896,0.000931937,0.00007864145,0.000023770925,0.000023451737,0.020046594],"genre_scores_gemma":[0.9965816,0.000039689265,0.0005114503,0.0013671973,0.00088924734,0.000003830739,0.0000024045837,0.000026200614,0.00057834975],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9982539,0.0004889079,0.0004219716,0.00013434574,0.00054118654,0.000159725],"domain_scores_gemma":[0.99508923,0.0039091394,0.00044875435,0.00021363454,0.00025662992,0.0000826332],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0024007475,0.00017782333,0.00023986676,0.00010046077,0.000100393794,0.000085599284,0.000512399,0.000090974136,0.001106766],"category_scores_gemma":[0.0028383834,0.00011003167,0.0001582619,0.000085772386,0.00020039528,0.00021279673,0.00009283119,0.0004369891,0.0000838725],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0005134498,0.000084240906,0.0002568128,0.000012613261,0.0003235974,0.000039199855,0.0007308816,0.0000018725234,0.0009685382,0.97494787,0.013307984,0.008812959],"study_design_scores_gemma":[0.00042546474,0.00009906344,0.0006048526,0.00017761852,0.00004248929,0.0015111383,0.0004306287,0.0000049986525,0.0097704865,0.97458327,0.012221832,0.00012817442],"about_ca_topic_score_codex":5.0358534e-7,"about_ca_topic_score_gemma":0.0000017531628,"teacher_disagreement_score":0.02384432,"about_ca_system_score_codex":0.000042483538,"about_ca_system_score_gemma":0.000034159126,"threshold_uncertainty_score":0.99980634},"labels":[],"label_agreement":null},{"id":"W1522344093","doi":"10.1142/s1793042116501335","title":"On the least prime ideal and Siegel zeros","year":2016,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","keywords":"Ideal (ethics); Mathematics; Prime (order theory); Combinatorics; Prime ideal; Coprime integers","score_opus":0.04302535173780385,"score_gpt":0.35433641416007033,"score_spread":0.31131106242226647,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1522344093","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9194567,0.000057537218,0.022496918,0.01450021,0.000741565,0.00020123541,0.000097204866,0.000031347292,0.04241725],"genre_scores_gemma":[0.989533,0.000028471115,0.0004479861,0.00042740922,0.00044565878,0.0000034467396,4.6874504e-7,0.000026128184,0.009087404],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99805206,0.00035541126,0.00041481954,0.00012259047,0.0008709117,0.00018421063],"domain_scores_gemma":[0.99208623,0.006806492,0.00033493649,0.00020656236,0.0004609077,0.00010486905],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0023311572,0.00012964575,0.0001862429,0.000093157076,0.00006036438,0.00006359971,0.0007019858,0.000052448562,0.0116660455],"category_scores_gemma":[0.003264434,0.000061768806,0.00013721235,0.000053353768,0.0002809492,0.00017443717,0.00014249337,0.00026365017,0.00047587827],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0005447826,0.00011377604,0.00068116136,0.0000035521994,0.0003834392,0.00008392841,0.0002681983,2.5210477e-7,0.0014804538,0.96125126,0.024895037,0.010294133],"study_design_scores_gemma":[0.0007617614,0.00005658151,0.0004611849,0.00023218682,0.000023689601,0.00066887133,0.00019598399,0.000008338378,0.0017217211,0.9922999,0.00348173,0.00008801895],"about_ca_topic_score_codex":0.000001233235,"about_ca_topic_score_gemma":0.0000010033036,"teacher_disagreement_score":0.070076294,"about_ca_system_score_codex":0.00011347617,"about_ca_system_score_gemma":0.00007988421,"threshold_uncertainty_score":0.9892374},"labels":[],"label_agreement":null},{"id":"W1555656750","doi":"10.1142/s1793042116500068","title":"A bias in Mertens’ product formula","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"York University","funders":"","keywords":"Mathematics; Product (mathematics); Sign (mathematics); Combinatorics; Mathematical analysis; Geometry","score_opus":0.19280901753121013,"score_gpt":0.42540032871782024,"score_spread":0.2325913111866101,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1555656750","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8809796,0.0002092907,0.006760676,0.0033981777,0.0019524362,0.00029562812,0.00004286196,0.000044451263,0.10631686],"genre_scores_gemma":[0.9887889,0.000012763348,0.00452554,0.00018473988,0.0006872097,0.000004822986,0.0000035573305,0.00003312977,0.0057593086],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9972806,0.0004140851,0.0007151091,0.00014306382,0.0012097439,0.00023741038],"domain_scores_gemma":[0.99671644,0.0012199882,0.0004144017,0.00022139406,0.0012484404,0.000179318],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.005122627,0.00014049704,0.00030850095,0.000300454,0.000016237056,0.0000575691,0.00084342685,0.000052587526,0.0019210333],"category_scores_gemma":[0.0070618056,0.000109543216,0.0001624129,0.00019364078,0.0001056794,0.00036663754,0.000141462,0.0004118949,0.00022928523],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0023850454,0.0011283397,0.023527602,0.000031596857,0.00095419894,0.0019333074,0.0052252426,0.000046800415,0.00022187097,0.8416472,0.10593324,0.016965523],"study_design_scores_gemma":[0.0014524704,0.00004846787,0.00034885685,0.00015085319,0.000024364455,0.0015173304,0.0011143282,0.00010070988,0.0004566247,0.98228854,0.012368401,0.00012903768],"about_ca_topic_score_codex":0.00001275734,"about_ca_topic_score_gemma":0.000014759109,"teacher_disagreement_score":0.14064132,"about_ca_system_score_codex":0.0003015952,"about_ca_system_score_gemma":0.0002980008,"threshold_uncertainty_score":0.9989914},"labels":[],"label_agreement":null},{"id":"W1621680326","doi":"10.1142/s1793042116500615","title":"Long unsplittable zero-sum sequences over a finite cyclic group","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Brock University","funders":"Natural Sciences and Engineering Research Council of Canada; Brock University","keywords":"Mathematics; Zero (linguistics); Combinatorics; Subsequence; Order (exchange); Sequence (biology); Cyclic group; Integer (computer science); Zero divisor; Bounded function; Mathematical analysis; Abelian group","score_opus":0.08264140736314521,"score_gpt":0.3850729380895467,"score_spread":0.3024315307264015,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1621680326","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8790198,0.00036502353,0.046539046,0.0008649758,0.0030942871,0.0002526488,0.00016462826,0.00008991841,0.06960967],"genre_scores_gemma":[0.9878346,0.000035083398,0.005591666,0.0003488842,0.00087051577,0.000008493076,0.000015757923,0.000052516207,0.005242498],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99662817,0.0005421822,0.0007479446,0.00018751323,0.0015604657,0.0003337541],"domain_scores_gemma":[0.99484366,0.0030723298,0.00057391444,0.00027112855,0.0009685358,0.0002704515],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0040322184,0.00020358605,0.00033086096,0.0002758885,0.00005157973,0.00017384719,0.0012042831,0.00011292381,0.004324043],"category_scores_gemma":[0.0036516788,0.00016603208,0.00023071317,0.0002019782,0.0002133559,0.00072498276,0.00022150652,0.0005387274,0.0003928826],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0019205259,0.0007251803,0.017793788,0.00004821153,0.0010970911,0.0015199055,0.0024780736,0.0001141059,0.00070794544,0.9234924,0.044731647,0.0053711403],"study_design_scores_gemma":[0.0013447623,0.00011750438,0.00073710404,0.00022206729,0.000039065548,0.0008896433,0.00039637482,0.0001152516,0.0003230482,0.9833985,0.012225757,0.00019091366],"about_ca_topic_score_codex":0.00001642549,"about_ca_topic_score_gemma":0.000010150538,"teacher_disagreement_score":0.10881478,"about_ca_system_score_codex":0.00031065132,"about_ca_system_score_gemma":0.00020405593,"threshold_uncertainty_score":0.99658614},"labels":[],"label_agreement":null},{"id":"W1632722589","doi":"10.1142/s1793042115500761","title":"Amicable pairs and aliquot cycles on average","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Lethbridge","funders":"","keywords":"Function (biology); Elliptic curve; Order (exchange); Upper and lower bounds; Generating function","score_opus":0.04224231027477038,"score_gpt":0.32679799849954366,"score_spread":0.2845556882247733,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1632722589","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9270368,0.00009182942,0.0038652308,0.00093610917,0.0012810623,0.00006585583,0.00003781974,0.00003352091,0.066651724],"genre_scores_gemma":[0.9938393,0.000022864237,0.002267776,0.0005686619,0.0005364853,0.0000017327945,0.0000036378613,0.00002244246,0.002737076],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.998522,0.00023420964,0.00040385235,0.00011644618,0.0005806733,0.00014284397],"domain_scores_gemma":[0.99769753,0.0012846275,0.00034831715,0.00013713178,0.00036639103,0.00016600562],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0017441888,0.00013744722,0.00022118808,0.00013351158,0.000034227316,0.00005495932,0.0003837035,0.000070490474,0.0016806076],"category_scores_gemma":[0.0014581125,0.00010980817,0.0001077557,0.00006413913,0.000104366816,0.00024243831,0.0000850102,0.00025862842,0.00012637187],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.001163082,0.0003608952,0.0020707631,0.000013428166,0.00050575065,0.0003026314,0.0016301898,0.00003311944,0.00009508146,0.9491666,0.037566923,0.0070915343],"study_design_scores_gemma":[0.00096862286,0.00009795105,0.00040683584,0.00012121079,0.000027362425,0.0009678216,0.0007850445,0.000016851323,0.00089544436,0.98349094,0.012094684,0.00012720718],"about_ca_topic_score_codex":0.0000023974007,"about_ca_topic_score_gemma":5.998787e-7,"teacher_disagreement_score":0.06680247,"about_ca_system_score_codex":0.00008417118,"about_ca_system_score_gemma":0.000058777663,"threshold_uncertainty_score":0.999232},"labels":[],"label_agreement":null},{"id":"W1714148690","doi":"10.1142/s1793042116501219","title":"On the heuristic of approximating polynomials over finite fields by random mappings","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Chebyshev polynomials; Finite field; Degree (music); Polynomial; Difference polynomials; Orthogonal polynomials; Random graph; Gegenbauer polynomials","score_opus":0.049687330715952674,"score_gpt":0.3193064656818408,"score_spread":0.26961913496588813,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1714148690","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8412498,0.00011299668,0.10309719,0.0020972104,0.0014791404,0.00018481053,0.00011635201,0.000020766578,0.051641684],"genre_scores_gemma":[0.9965451,0.0000036801366,0.0012489255,0.00055230194,0.00026306786,0.0000028556074,0.0000029654161,0.000011935144,0.0013692172],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9983968,0.00022983363,0.0006038359,0.00007235536,0.0005929736,0.00010416465],"domain_scores_gemma":[0.9935491,0.0051430156,0.0007448103,0.00014082024,0.00036555933,0.000056680536],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0019962376,0.000105480256,0.00024115668,0.00007857669,0.000028703971,0.000041650914,0.0005457543,0.00005244442,0.0025466098],"category_scores_gemma":[0.0050076735,0.00006847221,0.00015889162,0.000071199516,0.000055559984,0.00009635841,0.00007073392,0.00022756177,0.000029275776],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0016441776,0.00044478648,0.00043592628,0.000032601365,0.00073299423,0.000043065855,0.0022465726,0.00017526592,0.00044441913,0.71083295,0.28142285,0.0015443638],"study_design_scores_gemma":[0.0016337832,0.000085381515,0.000053168857,0.00018795344,0.000038008468,0.00011346435,0.0005131786,0.00031863153,0.00090509903,0.99133694,0.0047214553,0.000092952614],"about_ca_topic_score_codex":0.0000057469247,"about_ca_topic_score_gemma":5.121806e-7,"teacher_disagreement_score":0.28050396,"about_ca_system_score_codex":0.000038901282,"about_ca_system_score_gemma":0.000045154036,"threshold_uncertainty_score":0.9983652},"labels":[],"label_agreement":null},{"id":"W1753383004","doi":"10.1142/s1793042116500822","title":"Liouville identities with two functions","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Experimental and Theoretical Physics Studies","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Series (stratigraphy); Convolution (computer science); Power series; Pure mathematics; Lambert W function; Algebra over a field; Mathematical analysis; Computer science","score_opus":0.010592765304710924,"score_gpt":0.28885472685763697,"score_spread":0.27826196155292604,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1753383004","genre_codex":"other","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.07869772,0.000058455622,0.013231915,0.00023067437,0.00096693094,0.000028694125,0.00006356009,0.000008752852,0.9067133],"genre_scores_gemma":[0.99498093,8.835629e-7,0.000280824,0.000060094906,0.0009894879,0.0000032557928,0.000009509821,0.000008533845,0.0036664512],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99935883,0.00003813843,0.00016444214,0.00005623254,0.00030245812,0.00007987264],"domain_scores_gemma":[0.99924165,0.00008492345,0.00013185914,0.000052334297,0.0004166625,0.00007257555],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00014258045,0.00007609535,0.0001057444,0.000033910204,0.000036214788,0.000046404628,0.0001827226,0.0000067923265,0.0026031765],"category_scores_gemma":[0.000009397974,0.00005254622,0.00008022601,0.00004216393,0.00013414369,0.00022273435,0.000058052403,0.00010133555,0.00016292676],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00019117814,0.00015597774,0.0064678034,4.716806e-7,0.0004944359,0.000012768035,0.00055405276,0.000050521983,0.000055051285,0.9818224,0.0092540085,0.00094134087],"study_design_scores_gemma":[0.0008721185,0.00006162059,0.0000674933,0.000030531428,0.000026240328,0.0000420064,0.0043023825,0.0000047358326,0.0007589557,0.9889479,0.0048094983,0.00007651845],"about_ca_topic_score_codex":0.000013264851,"about_ca_topic_score_gemma":4.836017e-7,"teacher_disagreement_score":0.91628325,"about_ca_system_score_codex":0.000031090945,"about_ca_system_score_gemma":0.000043314743,"threshold_uncertainty_score":0.9983086},"labels":[],"label_agreement":null},{"id":"W1821687765","doi":"10.1142/s1793042115501158","title":"Quartic residuacity and the quadratic character of certain quadratic irrationalities","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Theories","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Legendre symbol; Quartic function; Mathematics; Binary quadratic form; Quadratic equation; Character (mathematics); Quadratic residue; Isotropic quadratic form; Quartic surface; Prime (order theory); Pure mathematics; Symbol (formal); Discriminant; Quadratic function; Discrete mathematics; Combinatorics; Geometry","score_opus":0.0648776301531123,"score_gpt":0.36775505466688857,"score_spread":0.30287742451377625,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1821687765","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.867053,0.0004284351,0.10723556,0.009700193,0.0013380499,0.0005002778,0.00010298857,0.000047040918,0.013594493],"genre_scores_gemma":[0.98504007,0.000015241639,0.012643358,0.00031686397,0.00033056308,0.000011254503,0.0000031163659,0.000021958813,0.0016175533],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9974251,0.00058315485,0.0009320391,0.00009772052,0.00082821446,0.0001337863],"domain_scores_gemma":[0.99172163,0.0061808936,0.0008522925,0.00019873538,0.00095040194,0.000096030184],"candidate_categories":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.0031176757,0.0001513663,0.0004211808,0.0000772697,0.00004264063,0.000060516086,0.00042132655,0.000052943084,0.00056573376],"category_scores_gemma":[0.008725323,0.00009192048,0.00013894383,0.00007457367,0.00063623604,0.00041607654,0.0000852031,0.00022035546,0.0000191421],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00086271093,0.00011246614,0.00012611998,0.000043873173,0.00025505855,0.000013560186,0.007104251,0.000008679823,0.00007871599,0.9897493,0.0012867822,0.00035845305],"study_design_scores_gemma":[0.0015523725,0.00004833833,0.00010808815,0.00018260212,0.000073749376,0.0003255056,0.003374254,0.00010468762,0.0005824208,0.99296063,0.00059184176,0.000095488445],"about_ca_topic_score_codex":0.000005011728,"about_ca_topic_score_gemma":0.0000041030607,"teacher_disagreement_score":0.117987126,"about_ca_system_score_codex":0.00006898277,"about_ca_system_score_gemma":0.00012564528,"threshold_uncertainty_score":0.9996246},"labels":[],"label_agreement":null},{"id":"W1830103037","doi":"10.1142/s1793042105000091","title":"THE CONVOLUTION SUM $\\sum\\limits_{m&lt;n/9}\\sigma(m)\\sigma(n-9m)$","year":2005,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":35,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Sigma; Combinatorics; Convolution (computer science); Physics; Quantum mechanics","score_opus":0.0417070806920368,"score_gpt":0.36865136428768563,"score_spread":0.3269442835956488,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1830103037","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.40764794,0.0030969004,0.15530665,0.041433733,0.010900518,0.0014071387,0.000406581,0.00038272436,0.3794178],"genre_scores_gemma":[0.9671689,0.00029007887,0.0032366805,0.0005255037,0.0030447019,0.000012669427,0.000010399025,0.00007536728,0.02563566],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9955584,0.0007228014,0.0011495976,0.00023840636,0.0018359384,0.00049487065],"domain_scores_gemma":[0.9919034,0.004990633,0.0008739901,0.0004584176,0.0015459703,0.00022754965],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0052058483,0.00027576854,0.00037896607,0.00019806018,0.00026603646,0.00024193861,0.001830206,0.00014426689,0.0060856617],"category_scores_gemma":[0.0032651809,0.00019063575,0.000438768,0.00018787706,0.00044352564,0.0005731612,0.00025404675,0.0007807606,0.0006290285],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0009807299,0.0003584116,0.0009209976,0.000013534251,0.0011030928,0.00012415729,0.00067503215,0.00006416676,0.00030620818,0.863953,0.10035657,0.031144131],"study_design_scores_gemma":[0.001361202,0.00006396413,0.00036979406,0.0001758731,0.000112025344,0.0012593048,0.00082793366,0.0006974844,0.0009385529,0.7396655,0.25426707,0.0002612972],"about_ca_topic_score_codex":0.000005392443,"about_ca_topic_score_gemma":0.000031934105,"teacher_disagreement_score":0.559521,"about_ca_system_score_codex":0.0005312663,"about_ca_system_score_gemma":0.00028157324,"threshold_uncertainty_score":0.9948229},"labels":[],"label_agreement":null},{"id":"W1842364091","doi":"10.1142/s1793042116500494","title":"A note on q-analogues of Dirichlet L-functions","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Algebraic number; Transcendental number; Dirichlet distribution; Combinatorics; Pure mathematics; Mathematical analysis","score_opus":0.09545783303944597,"score_gpt":0.40880916982188004,"score_spread":0.3133513367824341,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1842364091","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.4889356,0.00014158171,0.11675692,0.004249842,0.00393865,0.00033062047,0.00052086107,0.00008154334,0.3850444],"genre_scores_gemma":[0.988031,0.000008917089,0.0032472673,0.00018689055,0.00062795216,0.000002825915,0.000009328222,0.00002906331,0.007856753],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99737376,0.00035940198,0.0006695264,0.00011596171,0.0013171593,0.00016420527],"domain_scores_gemma":[0.9950226,0.002291537,0.0005980354,0.00023750169,0.001675513,0.00017483252],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0026105111,0.0001330189,0.00031647744,0.0002688614,0.000025487272,0.00003062407,0.00072129373,0.00006879845,0.002660353],"category_scores_gemma":[0.004587217,0.00010288415,0.00026172725,0.00015598527,0.00017346653,0.0001916632,0.000103646795,0.00035198973,0.00033596417],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0022441724,0.0010637838,0.0026131866,0.000020908858,0.0014810598,0.0002813422,0.0020244278,0.00010003566,0.00033159167,0.8127468,0.17110685,0.005985826],"study_design_scores_gemma":[0.0010899234,0.00018671359,0.00019095579,0.00016111524,0.00008799319,0.00046028727,0.0009526664,0.00006996571,0.00081319176,0.9777185,0.018151373,0.00011731795],"about_ca_topic_score_codex":0.0000075435228,"about_ca_topic_score_gemma":0.000004705415,"teacher_disagreement_score":0.4990954,"about_ca_system_score_codex":0.00020052072,"about_ca_system_score_gemma":0.00022865486,"threshold_uncertainty_score":0.9982514},"labels":[],"label_agreement":null},{"id":"W1876603738","doi":"10.1142/s1793042116500780","title":"A small value estimate in dimension two involving translations by rational points","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Meromorphic and Entire Functions","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Ottawa","funders":"","keywords":"Mathematics; Dimension (graph theory); Degree (music); Zero (linguistics); Algebraic number; Statement (logic); Combinatorics; Pure mathematics; Mathematical analysis","score_opus":0.08812298130373573,"score_gpt":0.3538501429021785,"score_spread":0.26572716159844273,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1876603738","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8079715,0.0002348186,0.17133822,0.0040108147,0.0029597965,0.00018888176,0.00015515865,0.00004695587,0.013093889],"genre_scores_gemma":[0.9630786,0.000013514067,0.034877,0.00033526254,0.00035937337,0.0000074763725,0.00006260886,0.000028890616,0.0012372484],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9983943,0.00021990598,0.0006002084,0.00010836656,0.0005444235,0.00013276604],"domain_scores_gemma":[0.9982191,0.00074977364,0.00031538683,0.00009759751,0.0004952909,0.00012286493],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0014010227,0.00011726714,0.00018560834,0.00015659211,0.00003971371,0.000046003723,0.0002588645,0.00005229333,0.0012833482],"category_scores_gemma":[0.00096801826,0.000104243976,0.000105747284,0.00010513178,0.000051023784,0.00029684458,0.00003514032,0.0002494218,0.000070047856],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00064320775,0.00097549934,0.010612634,0.000015590416,0.0004266683,0.00019231085,0.004151971,0.0017268431,0.0018629584,0.873388,0.10358817,0.002416134],"study_design_scores_gemma":[0.0025077644,0.00004581976,0.000592987,0.00024924477,0.00005350196,0.0005945066,0.0003821592,0.002734389,0.00031294656,0.9875313,0.004835485,0.0001599041],"about_ca_topic_score_codex":0.000026201998,"about_ca_topic_score_gemma":0.00003814296,"teacher_disagreement_score":0.15510716,"about_ca_system_score_codex":0.00014924812,"about_ca_system_score_gemma":0.00015754157,"threshold_uncertainty_score":0.9996296},"labels":[],"label_agreement":null},{"id":"W1886513500","doi":"10.1142/s1793042116500378","title":"Radical of perfect numbers and perfect numbers among polynomial values","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Conjecture; Perfect power; Combinatorics; Degree (music); Integer (computer science); Polynomial; Upper and lower bounds; Discrete mathematics; Mathematical analysis","score_opus":0.04793871021196789,"score_gpt":0.3673986485949383,"score_spread":0.31945993838297043,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1886513500","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9598733,0.000118304655,0.0015901558,0.00034945345,0.0008590819,0.00014002757,0.000048343663,0.00002530447,0.036996037],"genre_scores_gemma":[0.99294657,0.000038972117,0.003035094,0.00008052024,0.0008322288,0.0000037528257,0.0000056834956,0.00005571318,0.0030014748],"study_design_codex":"observational","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9959706,0.00084050506,0.0009683369,0.0002439718,0.0016396306,0.00033693528],"domain_scores_gemma":[0.99487495,0.0026285152,0.00076083775,0.00027509264,0.0010196796,0.0004409197],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0047864383,0.00026664452,0.00060817145,0.0002707695,0.000057392917,0.00008738547,0.000900655,0.0001625864,0.0027844226],"category_scores_gemma":[0.0041058897,0.00022231175,0.000361572,0.0001629587,0.00095385424,0.00048358153,0.00025365158,0.0006187678,0.00006413618],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.011332331,0.0022793883,0.33612707,0.0002636858,0.008099281,0.0017666387,0.022972934,0.000082618615,0.0017202953,0.28660738,0.31325293,0.015495439],"study_design_scores_gemma":[0.007636538,0.00057739654,0.0054503693,0.00080797414,0.00050637964,0.005375133,0.008111295,0.00046406692,0.003024358,0.958933,0.008360297,0.0007531824],"about_ca_topic_score_codex":0.00008703035,"about_ca_topic_score_gemma":0.000015285008,"teacher_disagreement_score":0.6723256,"about_ca_system_score_codex":0.000288951,"about_ca_system_score_gemma":0.00035780613,"threshold_uncertainty_score":0.99812716},"labels":[],"label_agreement":null},{"id":"W1950023722","doi":"10.1142/s1793042118500951","title":"Subconvexity for a double Dirichlet series and non-vanishing of L-functions","year":2017,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"York University","funders":"","keywords":"Dirichlet series; Convexity; Mathematics; Combinatorics; Upper and lower bounds; Dirichlet distribution; Integer (computer science); Quadratic equation; Function (biology); Series (stratigraphy); Mathematical analysis; Geometry; Computer science","score_opus":0.0862837702492847,"score_gpt":0.41041344211486186,"score_spread":0.3241296718655772,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1950023722","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7290759,0.00050360645,0.19662923,0.004064445,0.0075932546,0.0014732687,0.002604264,0.00006182782,0.057994183],"genre_scores_gemma":[0.97394305,0.00013918341,0.012541667,0.00004125498,0.0012082657,0.000036970985,0.00004185275,0.000069039015,0.011978711],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99764955,0.0001559039,0.00090890727,0.00025020022,0.00081426697,0.00022117137],"domain_scores_gemma":[0.9934826,0.0019103243,0.001935766,0.0004851948,0.0020545316,0.00013161251],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0033608743,0.0002582134,0.0006889601,0.00021680935,0.00013340986,0.00024705665,0.0013563682,0.00023523664,0.0009308735],"category_scores_gemma":[0.0023686301,0.00022560591,0.00045563525,0.000032429438,0.00043056367,0.00042529433,0.00087648147,0.000803875,0.000010497613],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.013252246,0.0010034525,0.01034473,0.0016782781,0.009271007,0.00024071922,0.004652487,0.00006517973,0.0006395257,0.8939253,0.058724567,0.0062025157],"study_design_scores_gemma":[0.0014546979,0.000081136735,0.0003562381,0.0008365741,0.00025162057,0.00040236683,0.0006056099,0.000084023966,0.00076412363,0.9911282,0.00383237,0.0002030044],"about_ca_topic_score_codex":0.000029610106,"about_ca_topic_score_gemma":0.000020328922,"teacher_disagreement_score":0.24486713,"about_ca_system_score_codex":0.00015032075,"about_ca_system_score_gemma":0.00041430644,"threshold_uncertainty_score":0.9999824},"labels":[],"label_agreement":null},{"id":"W1967002960","doi":"10.1142/s1793042110003290","title":"MULTIPLICATIVE ORDER OF GAUSS PERIODS","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":31,"is_retracted":false,"has_abstract":true,"route_ca_aff":false,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"","funders":"University of Waterloo","keywords":"Mathematics; Multiplicative function; Upper and lower bounds; Gauss; Order (exchange); Gauss sum; Pure mathematics; Mathematical analysis; Physics","score_opus":0.006283978535805887,"score_gpt":0.27889246631938786,"score_spread":0.272608487783582,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1967002960","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.51656115,0.00004529383,0.4571137,0.0012443385,0.0036299636,0.0000652134,0.000028322898,0.00003488899,0.021277113],"genre_scores_gemma":[0.96527374,0.0000070457077,0.034144774,0.00019740529,0.00022764396,0.0000016325705,9.040259e-7,0.000005642157,0.00014124287],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9989982,0.0000998164,0.00032969235,0.000106466476,0.00037174136,0.00009404766],"domain_scores_gemma":[0.9979523,0.00044572444,0.00039980444,0.00022464071,0.00091446773,0.000063078915],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00080966053,0.00008302525,0.00013352331,0.00014254365,0.00003138354,0.000054518747,0.0015716644,0.00004512563,0.0013062969],"category_scores_gemma":[0.00030709934,0.000067221685,0.00015965631,0.00017846379,0.00014339498,0.00037944244,0.00015704887,0.00029031318,0.000028300896],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0001218704,0.0001697501,0.0024878131,0.0000023000703,0.00017990611,0.00002555617,0.0014823792,0.000009620783,0.01264712,0.9368927,0.0006539704,0.045327026],"study_design_scores_gemma":[0.0012231038,0.00014159465,0.013590792,0.00009777317,0.000023117018,0.0011318208,0.00030023916,0.0005407782,0.019638078,0.9130316,0.05001756,0.00026356275],"about_ca_topic_score_codex":0.0000019942956,"about_ca_topic_score_gemma":0.0000017374759,"teacher_disagreement_score":0.44871256,"about_ca_system_score_codex":0.000011115285,"about_ca_system_score_gemma":0.000071876835,"threshold_uncertainty_score":0.99960667},"labels":[],"label_agreement":null},{"id":"W1968640148","doi":"10.1142/s1793042112500200","title":"UPPER BOUNDS FOR THE NUMBER OF SOLUTIONS TO QUARTIC THUE EQUATIONS","year":2011,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"Mathematisches Forschungsinstitut Oberwolfach","keywords":"Quartic function; Logarithm; Thue equation; Mathematics; Okazaki fragments; Upper and lower bounds; Signature (topology); Work (physics); Applied mathematics; Discrete mathematics; Pure mathematics; Mathematical analysis; Physics; Diophantine equation; Quantum mechanics; Geometry","score_opus":0.07856317179934023,"score_gpt":0.36860746610874073,"score_spread":0.2900442943094005,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1968640148","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.106111534,0.00034353745,0.8518853,0.0040121777,0.00964071,0.0010583135,0.001263047,0.00005972932,0.025625642],"genre_scores_gemma":[0.9788429,0.000041577397,0.015486438,0.00042605912,0.0014028309,0.000116833144,0.000031607204,0.0000718836,0.0035798715],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99685603,0.00035299273,0.0013689531,0.0002544098,0.0008336774,0.00033391523],"domain_scores_gemma":[0.9881922,0.0076066824,0.0014793592,0.00060364185,0.0019687053,0.00014939635],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0036249845,0.0003227497,0.0005690945,0.00023935876,0.00016812365,0.00009069285,0.0018591079,0.00025912808,0.008515775],"category_scores_gemma":[0.0046404577,0.00023732136,0.0008975557,0.00015884568,0.00025449446,0.00018520931,0.0006232381,0.00074385304,0.00018425567],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00057932443,0.00048200268,0.0003668591,0.00007713084,0.0021905354,0.000008141533,0.003720541,0.0001201159,0.00005178978,0.9720588,0.018027171,0.0023176065],"study_design_scores_gemma":[0.00051969226,0.000044917735,0.00036686411,0.00045874302,0.00047746283,0.00021401107,0.0010759536,0.00007746459,0.0003697736,0.99072295,0.0054280735,0.00024410474],"about_ca_topic_score_codex":0.000022778902,"about_ca_topic_score_gemma":0.000009139218,"teacher_disagreement_score":0.8727314,"about_ca_system_score_codex":0.0001825322,"about_ca_system_score_gemma":0.00039760728,"threshold_uncertainty_score":0.9923906},"labels":[],"label_agreement":null},{"id":"W1970377478","doi":"10.1142/s1793042113500140","title":"NONZERO VALUES OF DIRICHLET L-FUNCTIONS IN VERTICAL ARITHMETIC PROGRESSIONS","year":2013,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Lethbridge; University of British Columbia","funders":"Banff International Research Station for Mathematical Innovation and Discovery","keywords":"Arithmetic progression; Mathematics; Dirichlet series; Conjecture; Function (biology); Zero (linguistics); Arithmetic function; Dirichlet distribution; Arithmetic; Dirichlet L-function; Analytic number theory; Combinatorics; Upper and lower bounds; Rational number; Pure mathematics; Discrete mathematics; Mathematical analysis","score_opus":0.0581562815653314,"score_gpt":0.4042029761591408,"score_spread":0.34604669459380943,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1970377478","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9442106,0.00032538277,0.02360509,0.0019633453,0.0032718482,0.00070150656,0.00032349856,0.000048314447,0.025550453],"genre_scores_gemma":[0.9865173,0.000063568965,0.0090922825,0.0000648308,0.0006673557,0.00004645772,0.000029494133,0.000070969225,0.0034477215],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9951456,0.0008626194,0.0016576272,0.00029770195,0.0017001163,0.000336326],"domain_scores_gemma":[0.99277985,0.0038208102,0.00085088395,0.000500477,0.0018485418,0.00019942022],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0028128435,0.00031994114,0.0008085536,0.00064553693,0.000038003767,0.00010120249,0.0016607695,0.00032794185,0.008967893],"category_scores_gemma":[0.0050778957,0.00025739038,0.0005432104,0.00020048062,0.0004471502,0.00021701425,0.0010393868,0.001779872,0.00018386767],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0023622378,0.0078663835,0.043888625,0.00078205473,0.0072537092,0.0012980413,0.005100385,0.00057156367,0.0006708101,0.817355,0.09782365,0.015027594],"study_design_scores_gemma":[0.00080466113,0.00006185998,0.0016714295,0.0018500203,0.00017345032,0.0003299777,0.00059153757,0.00056321453,0.0002906339,0.99277,0.00066163065,0.00023155013],"about_ca_topic_score_codex":0.000027201697,"about_ca_topic_score_gemma":0.000007308298,"teacher_disagreement_score":0.17541508,"about_ca_system_score_codex":0.00038005123,"about_ca_system_score_gemma":0.0005302573,"threshold_uncertainty_score":0.99998784},"labels":[],"label_agreement":null},{"id":"W1970528605","doi":"10.1142/s1793042110002843","title":"CYCLIC SEXTIC TRINOMIALS x<sup>6</sup> + Ax + B","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Okanagan University College; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"","keywords":"Trinomial; Mathematics; Combinatorics; Scaling; Pure mathematics; Type (biology); Genus; Geometry; Botany","score_opus":0.02022676424512003,"score_gpt":0.3173059908487807,"score_spread":0.29707922660366065,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1970528605","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9618842,0.000031648036,0.0024250583,0.0005700904,0.002239961,0.000097168064,0.0000502183,0.000044597,0.03265706],"genre_scores_gemma":[0.98880535,0.000016273138,0.003987938,0.00048673328,0.0022945434,0.0000054179272,0.0000075183157,0.000046140492,0.0043500545],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9975084,0.00029724065,0.00092628784,0.00019003234,0.00079697,0.00028103808],"domain_scores_gemma":[0.99527764,0.0028905421,0.000733297,0.00032832124,0.00057334243,0.00019684005],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002677546,0.00023840705,0.00041166026,0.0002604238,0.00007820004,0.00009988407,0.0011473516,0.00018049045,0.022949714],"category_scores_gemma":[0.003021539,0.0001989179,0.00038724512,0.00015023888,0.000189212,0.00043263411,0.00014092607,0.00087323267,0.00061199215],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0010069457,0.0007640902,0.003052063,0.00003334993,0.0012954072,0.00048040063,0.0022446946,0.00003607266,0.0038134877,0.9421856,0.025490472,0.01959742],"study_design_scores_gemma":[0.0013481731,0.000046988407,0.00051707885,0.000082025705,0.00009371523,0.0029943553,0.0005840949,0.000026505644,0.0037387628,0.95901126,0.031317335,0.00023972307],"about_ca_topic_score_codex":0.0000026692362,"about_ca_topic_score_gemma":0.000001596909,"teacher_disagreement_score":0.028307006,"about_ca_system_score_codex":0.000071756935,"about_ca_system_score_gemma":0.00012129167,"threshold_uncertainty_score":0.9779434},"labels":[],"label_agreement":null},{"id":"W1972477966","doi":"10.1142/s179304210900202x","title":"A GENERALIZATION OF THE SATO–TATE CONJECTURE","year":2009,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Conjecture; Sato–Tate conjecture; Generalization; Holomorphic function; Elliptic curve; Distribution (mathematics); Pure mathematics; Eigenvalues and eigenvectors; Combinatorics; Mathematical analysis; Modular elliptic curve; Quarter period","score_opus":0.016181156119908512,"score_gpt":0.30710078502171023,"score_spread":0.29091962890180173,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1972477966","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.970693,0.000110811365,0.012688148,0.0019280394,0.0015352283,0.00010022413,0.00004354615,0.00001647463,0.012884528],"genre_scores_gemma":[0.996084,0.00001696741,0.0014644079,0.0007239715,0.0003969455,5.8613347e-7,0.0000028902823,0.000010957292,0.0012992729],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99848795,0.00025532796,0.0005323375,0.00007711059,0.00054175634,0.00010553494],"domain_scores_gemma":[0.9980879,0.0004892801,0.0007581493,0.00017461984,0.00044709575,0.000042985124],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008699142,0.000111793524,0.00020091105,0.00008308998,0.000038230035,0.000020546688,0.0006435377,0.000068942034,0.001589775],"category_scores_gemma":[0.0008290038,0.000071430266,0.00024154948,0.00014912258,0.000083355386,0.00015285576,0.000043160668,0.00021100497,0.000012794212],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00023932496,0.00023062124,0.0013285365,0.000010771041,0.00032741085,0.000029529161,0.0011870142,0.00007036865,0.0017265459,0.97461015,0.010955146,0.0092845615],"study_design_scores_gemma":[0.00056786556,0.000041404845,0.0023493087,0.0001267257,0.000051338222,0.000605875,0.00019895787,0.000011739742,0.00864247,0.9832894,0.0040340433,0.00008083983],"about_ca_topic_score_codex":0.0000012174258,"about_ca_topic_score_gemma":8.3873226e-7,"teacher_disagreement_score":0.025391001,"about_ca_system_score_codex":0.00004650665,"about_ca_system_score_gemma":0.0000640581,"threshold_uncertainty_score":0.9993229},"labels":[],"label_agreement":null},{"id":"W1974492627","doi":"10.1142/s179304211530001x","title":"Generalized Fermat equations: A miscellany","year":2014,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":40,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Lethbridge; Simon Fraser University; University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; Nederlandse Organisatie voor Wetenschappelijk Onderzoek","keywords":"Mathematics; Fermat's Last Theorem; Fermat number; Descent (aeronautics); Coprime integers; Fermat's little theorem; Fermat's theorem on sums of two squares; Exponent; Wieferich prime; Modularity (biology); Combinatorics; Discrete mathematics; Pure mathematics","score_opus":0.02944396120429895,"score_gpt":0.3209703101396801,"score_spread":0.29152634893538115,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1974492627","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.6584026,0.00017094632,0.21269721,0.0024198908,0.004560066,0.00017903653,0.00006399674,0.00010560019,0.12140062],"genre_scores_gemma":[0.98260576,0.000019977884,0.009739998,0.0008582803,0.0012927657,0.0000045823504,0.000010717536,0.00003111555,0.0054368153],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9979334,0.00046876736,0.0006597813,0.000119777986,0.0006453781,0.00017291441],"domain_scores_gemma":[0.99581546,0.0027345978,0.000580996,0.00020597552,0.00055195455,0.00011101625],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002141376,0.00015511383,0.00027443568,0.0001592881,0.00005903716,0.00006627955,0.0006910433,0.00008288853,0.01224467],"category_scores_gemma":[0.0030964874,0.00012711354,0.00025377408,0.00009601698,0.00008426598,0.00019122074,0.00007748961,0.000245405,0.00037149203],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00027338555,0.00018099902,0.00026362488,0.00001187747,0.00036526268,0.000042424588,0.0004159843,0.000013523153,0.00035938484,0.9724616,0.01999902,0.005612932],"study_design_scores_gemma":[0.0010407649,0.000032271168,0.000093188086,0.000092714996,0.000053226293,0.00061398774,0.00016877051,0.0000969226,0.0010799164,0.9555085,0.04107619,0.00014358135],"about_ca_topic_score_codex":0.0000017192333,"about_ca_topic_score_gemma":9.067086e-7,"teacher_disagreement_score":0.3242031,"about_ca_system_score_codex":0.00007328076,"about_ca_system_score_gemma":0.00004857029,"threshold_uncertainty_score":0.98865825},"labels":[],"label_agreement":null},{"id":"W1974642904","doi":"10.1142/s1793042105000212","title":"SIMULTANEOUS APPROXIMATION BY CONJUGATE ALGEBRAIC NUMBERS IN FIELDS OF TRANSCENDENCE DEGREE ONE","year":2005,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Meromorphic and Entire Functions","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Ottawa","funders":"","keywords":"Transcendental number; Mathematics; Degree (music); Bounded function; Zero (linguistics); Algebraic number; Algebraic extension; Complex conjugate; Transcendence (philosophy); Field (mathematics); Duality (order theory); Pure mathematics; Field extension; Discrete mathematics; Combinatorics; Mathematical analysis; Differential equation","score_opus":0.05632307839915406,"score_gpt":0.32407836435758264,"score_spread":0.26775528595842857,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1974642904","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7254286,0.0004955979,0.24183746,0.002266653,0.0040677227,0.0005448757,0.00083089335,0.00005384857,0.024474377],"genre_scores_gemma":[0.989354,0.00023781325,0.008332468,0.00014182723,0.00040011384,0.0000099316385,0.00007181896,0.000032388394,0.0014196518],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9972489,0.00023612898,0.0012690264,0.00020392385,0.0008670143,0.00017499598],"domain_scores_gemma":[0.99619263,0.001621653,0.0012570509,0.00023888402,0.0006069018,0.000082872386],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0010550647,0.00023381812,0.0005285876,0.0002002918,0.000022183407,0.000038260696,0.00076890463,0.00031898802,0.004669141],"category_scores_gemma":[0.0009817213,0.00022862204,0.0003015067,0.00007955764,0.000119666955,0.00016068078,0.00010945037,0.00096224505,0.000027017235],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.008686215,0.013962521,0.0060229464,0.0028966973,0.012868224,0.0015449642,0.035546895,0.027324941,0.007183062,0.5246007,0.14928433,0.21007851],"study_design_scores_gemma":[0.002249417,0.00010652648,0.0001908406,0.002719707,0.00032116668,0.0005372522,0.000625294,0.0025487884,0.0023474311,0.9853395,0.0024956332,0.00051839266],"about_ca_topic_score_codex":0.000047181387,"about_ca_topic_score_gemma":0.00006087229,"teacher_disagreement_score":0.46073887,"about_ca_system_score_codex":0.00019055611,"about_ca_system_score_gemma":0.00017694193,"threshold_uncertainty_score":0.99624074},"labels":[],"label_agreement":null},{"id":"W1976360479","doi":"10.1142/s1793042109002742","title":"BOUNDED STEP FUNCTIONS AND FACTORIAL RATIO SEQUENCES","year":2009,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":10,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Mathematics; Factorial; Bounded function; Quotient; Gravitational singularity; Sequence (biology); Factorial experiment; Square (algebra); Combinatorics; Upper and lower bounds; Discrete mathematics; Pure mathematics; Mathematical analysis; Statistics; Geometry","score_opus":0.011967821897041217,"score_gpt":0.26965936899694404,"score_spread":0.25769154709990283,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1976360479","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.09005044,0.0001098323,0.8871459,0.002495852,0.0053927284,0.000050376864,0.000015926224,0.00005254995,0.014686414],"genre_scores_gemma":[0.99378854,0.000019999632,0.0046956223,0.0005262109,0.0007308746,6.319537e-7,0.0000015783274,0.0000026148728,0.00023391139],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9990638,0.00012816033,0.00025149502,0.00010956631,0.00035249745,0.00009451023],"domain_scores_gemma":[0.99907166,0.00027423445,0.0002032401,0.00010848633,0.00027228953,0.000070078684],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00055854867,0.0000820199,0.00010323868,0.00012561875,0.00008022471,0.0002727784,0.00064390927,0.00003511106,0.00033522493],"category_scores_gemma":[0.00010659659,0.00006729139,0.00010087661,0.000109101675,0.00006528936,0.0007662181,0.00004803584,0.0001524197,0.000017172943],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0001175443,0.00006427069,0.00035240006,6.202015e-7,0.00009892956,0.000041946132,0.00055041484,0.000008963534,0.0006580832,0.93457246,0.0028313657,0.060702987],"study_design_scores_gemma":[0.0005227811,0.00016317025,0.0023804645,0.00003604248,0.00001282272,0.0006210197,0.00013151724,0.00016294482,0.00030020927,0.97073007,0.024825072,0.00011388631],"about_ca_topic_score_codex":0.0000011933472,"about_ca_topic_score_gemma":0.0000010159833,"teacher_disagreement_score":0.90373814,"about_ca_system_score_codex":0.000030119301,"about_ca_system_score_gemma":0.00006396257,"threshold_uncertainty_score":0.3670478},"labels":[],"label_agreement":null},{"id":"W1977131788","doi":"10.1142/s1793042110002880","title":"SEXTENARY QUADRATIC FORMS AND AN IDENTITY OF KLEIN AND FRICKE","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Integer (computer science); Quadratic equation; Identity (music); Combinatorics; Pure mathematics; Physics; Geometry","score_opus":0.0344447579013868,"score_gpt":0.40558074805459626,"score_spread":0.37113599015320947,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1977131788","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.99453056,0.000035651337,0.0016879911,0.00018155917,0.0002924834,0.000060721337,0.00003418501,0.000007063874,0.0031697908],"genre_scores_gemma":[0.99389607,0.000027364658,0.0054999557,0.00004977353,0.00022484848,0.0000015693583,0.0000026923476,0.000017483078,0.000280261],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99860954,0.0001634891,0.0004474575,0.00010001672,0.00056163175,0.00011788133],"domain_scores_gemma":[0.9977193,0.0012011434,0.0003494364,0.00015357239,0.00046149403,0.00011507745],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0023156428,0.00009806708,0.00020951661,0.00016205861,0.000036943624,0.00007082411,0.00042343503,0.0000705708,0.0013314208],"category_scores_gemma":[0.0012999732,0.00007529092,0.00006325521,0.000059912658,0.00024329277,0.0008577341,0.00014380766,0.0003996035,0.000008541763],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00041823718,0.0003000465,0.009205925,0.000055976638,0.00023332977,0.00009817238,0.0016630423,4.1012612e-7,0.012923939,0.9675759,0.00048768934,0.0070372964],"study_design_scores_gemma":[0.00057320856,0.000106467174,0.0058654747,0.000068059606,0.000024978066,0.0010377278,0.00063396385,0.000082768514,0.00098163,0.99026495,0.00027960594,0.00008114322],"about_ca_topic_score_codex":0.0000065379204,"about_ca_topic_score_gemma":0.000037835096,"teacher_disagreement_score":0.022689039,"about_ca_system_score_codex":0.000018623834,"about_ca_system_score_gemma":0.000049535814,"threshold_uncertainty_score":0.9995815},"labels":[],"label_agreement":null},{"id":"W1979322825","doi":"10.1142/s1793042113500474","title":"INTEGRAL POINTS ON CONGRUENT NUMBER CURVES","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Diophantine equation; Elliptic curve; Quartic function; Prime (order theory); Logarithm; Integer (computer science); Variety (cybernetics); Diophantine approximation; Pure mathematics; Combinatorics; Discrete mathematics; Mathematical analysis","score_opus":0.024385697660722162,"score_gpt":0.32382431961286023,"score_spread":0.29943862195213805,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1979322825","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8322194,0.00011401934,0.002676954,0.005538229,0.0042520557,0.0002973051,0.00007670202,0.00007464826,0.15475067],"genre_scores_gemma":[0.9860357,0.000085257445,0.0025247422,0.0039012332,0.00082825636,0.000014662957,0.000012884131,0.00004511462,0.0065521696],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9974494,0.00036894894,0.00080152176,0.00017647355,0.0009425747,0.00026110688],"domain_scores_gemma":[0.99576825,0.0021453665,0.00066766964,0.00025511388,0.0009827524,0.00018082824],"candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0014141408,0.00024515294,0.00036984734,0.00013693672,0.000051664992,0.00008533513,0.00089675334,0.00010257438,0.07895794],"category_scores_gemma":[0.0022127277,0.00018617314,0.00034416895,0.00012089956,0.00015436707,0.00050380605,0.000112659436,0.0005468578,0.003614191],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00037348646,0.0006283978,0.002960424,0.000045213135,0.0008360897,0.00014378881,0.00045220982,0.0000013444709,0.00009005058,0.69458306,0.2923734,0.007512556],"study_design_scores_gemma":[0.00085282704,0.00006982516,0.0016351743,0.00089615525,0.000051213872,0.001214538,0.0005116855,0.0000051293327,0.001182982,0.9813832,0.01197521,0.0002220519],"about_ca_topic_score_codex":0.000011098856,"about_ca_topic_score_gemma":0.0000010485891,"teacher_disagreement_score":0.28680015,"about_ca_system_score_codex":0.0001447673,"about_ca_system_score_gemma":0.000071887196,"threshold_uncertainty_score":0.9971616},"labels":[],"label_agreement":null},{"id":"W1983959066","doi":"10.1142/s1793042115500347","title":"Quaternionic modular forms and exceptional sets of hypergeometric functions","year":2014,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Champlain Regional College","funders":"","keywords":"Mathematics; Hypergeometric function; Modular form; Pure mathematics; Algebra over a field; Basic hypergeometric series; Eisenstein series; Hypergeometric distribution; Modular design; Generalized hypergeometric function; Computer science","score_opus":0.017550214596035733,"score_gpt":0.31546100647231845,"score_spread":0.2979107918762827,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1983959066","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.90625876,0.000075845965,0.09068681,0.00015403658,0.00054830906,0.00003356444,0.000043844862,0.000009475565,0.0021893543],"genre_scores_gemma":[0.9951468,0.000038777736,0.0037829892,0.0000747881,0.00026684208,0.0000018478845,0.000009258256,0.000014894596,0.00066377205],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99873805,0.000074997115,0.00047942533,0.00009457108,0.0005040634,0.000108899054],"domain_scores_gemma":[0.9979343,0.00094206416,0.0004683141,0.000108202075,0.00047538782,0.000071768285],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007436501,0.00010298613,0.00021303013,0.00034734645,0.000035863635,0.000018523644,0.00023861363,0.000054181844,0.0017403242],"category_scores_gemma":[0.0010794296,0.000080448226,0.0001378681,0.00016812848,0.00008067699,0.000280002,0.00006325493,0.00016484404,0.00003383098],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0003784256,0.00053771824,0.01759104,0.00006248283,0.0008215831,0.000021025367,0.00036147286,0.0003307768,0.0014311183,0.89441997,0.0027442058,0.081300214],"study_design_scores_gemma":[0.0007368927,0.000079902966,0.010653493,0.00007914894,0.00003904867,0.0005081128,0.00015434324,0.00013582052,0.00027684524,0.9839169,0.0033214744,0.00009805689],"about_ca_topic_score_codex":6.7045926e-7,"about_ca_topic_score_gemma":9.315196e-7,"teacher_disagreement_score":0.089496925,"about_ca_system_score_codex":0.000043495045,"about_ca_system_score_gemma":0.000027150967,"threshold_uncertainty_score":0.9991722},"labels":[],"label_agreement":null},{"id":"W1985682310","doi":"10.1142/s1793042113501170","title":"THE GROWTH OF THE SELMER GROUP OF AN ELLIPTIC CURVE WITH SPLIT MULTIPLICATIVE REDUCTION","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Multiplicative function; Elliptic curve; Prime (order theory); Pure mathematics; Reduction (mathematics); Prime factor; Group (periodic table); Good reduction; Algebraic number; Multiplicative group; Combinatorics; Mathematical analysis; Geometry","score_opus":0.013152119300995187,"score_gpt":0.2768783814258254,"score_spread":0.2637262621248302,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1985682310","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9937544,0.000042665375,0.0020347412,0.00045028768,0.00047765294,0.00019952506,0.000020710555,0.000007681459,0.0030123377],"genre_scores_gemma":[0.9963121,0.000019072564,0.0026285972,0.000041168783,0.00025238912,0.000010905603,0.0000022289114,0.000021422458,0.00071215746],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99798477,0.0004582343,0.0006382289,0.00011425814,0.0006685523,0.00013595533],"domain_scores_gemma":[0.995574,0.0014958533,0.0012899926,0.0003064817,0.0012751832,0.000058503883],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0013827776,0.00014019082,0.00022700378,0.00006749146,0.00008265156,0.00003063119,0.0009451968,0.000060778355,0.00082740985],"category_scores_gemma":[0.0006268747,0.00007047253,0.0001783363,0.00017348859,0.00046761517,0.00039652738,0.00008546197,0.00029982848,0.000019366273],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.001031068,0.00070520217,0.0031723399,0.00003952446,0.0012176158,0.000004788066,0.003322055,0.00001550361,0.005545095,0.97846353,0.0013272293,0.0051560462],"study_design_scores_gemma":[0.000697322,0.0001426386,0.011925167,0.0002010854,0.000089513735,0.00057048444,0.0026741717,0.00003819866,0.016490476,0.9668193,0.00024125086,0.00011040768],"about_ca_topic_score_codex":0.000020937765,"about_ca_topic_score_gemma":0.0000026933703,"teacher_disagreement_score":0.01164425,"about_ca_system_score_codex":0.000055635675,"about_ca_system_score_gemma":0.00005401732,"threshold_uncertainty_score":0.90595573},"labels":[],"label_agreement":null},{"id":"W1989341012","doi":"10.1142/s1793042112501539","title":"AN ASYMPTOTIC FORMULA FOR THE COEFFICIENTS OF j(z)","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Ramanujan's sum; Asymptotic formula; Laplace transform; Invariant (physics); Asymptotic expansion; Method of steepest descent; Asymptotic analysis; Descent (aeronautics); Partition (number theory); Mathematical analysis; Pure mathematics; Combinatorics; Mathematical physics","score_opus":0.04783556717829426,"score_gpt":0.40914903571424716,"score_spread":0.3613134685359529,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1989341012","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.15446953,0.0001571701,0.838935,0.00018291055,0.0018166951,0.00023155755,0.00009253184,0.000016369386,0.00409824],"genre_scores_gemma":[0.9786723,0.000009073172,0.01993908,0.00006425056,0.00048326462,0.0000067554947,0.0000021777578,0.000020644015,0.0008024194],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9987802,0.00006110663,0.0004913379,0.000045223216,0.00047497757,0.0001471617],"domain_scores_gemma":[0.99523014,0.0034412122,0.00051773054,0.00015401123,0.00059378607,0.00006314346],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001233562,0.0000850661,0.00017943488,0.000057531324,0.000037629947,0.000024311483,0.0005721452,0.00003437496,0.0008182712],"category_scores_gemma":[0.0018052642,0.000053361404,0.00016780161,0.000038548606,0.00010413349,0.0004342152,0.000044549615,0.000099611665,0.00001336759],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00016190317,0.00052224484,0.00035423832,0.000036679015,0.00029526398,0.0000016601739,0.0014278913,0.000055648976,0.00041756197,0.99238425,0.0020648194,0.0022778073],"study_design_scores_gemma":[0.0004794142,0.00004908412,0.00022642726,0.00010297352,0.000090494905,0.00015137656,0.0009276472,0.00021834845,0.0024175758,0.99288493,0.002384423,0.0000673091],"about_ca_topic_score_codex":5.2326874e-7,"about_ca_topic_score_gemma":4.98375e-7,"teacher_disagreement_score":0.8242028,"about_ca_system_score_codex":0.000050947983,"about_ca_system_score_gemma":0.000025664385,"threshold_uncertainty_score":0.89594954},"labels":[],"label_agreement":null},{"id":"W1989686124","doi":"10.1142/s179304211350070x","title":"LOCAL NEWFORMS AND FORMAL EXTERIOR SQUARE L-FUNCTIONS","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Square (algebra); Pure mathematics; Unitary state; Galois module; Field (mathematics); Zero (linguistics); Algebra over a field; Geometry","score_opus":0.013007462555914485,"score_gpt":0.29926390707336537,"score_spread":0.28625644451745086,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1989686124","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.69581443,0.000070873386,0.29755673,0.00046861,0.00078727957,0.00007375347,0.000025489848,0.000019159677,0.005183697],"genre_scores_gemma":[0.9923006,0.0000181054,0.0049698134,0.00027872948,0.0003640118,0.0000055395617,0.0000038527646,0.000015513779,0.0020438293],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9990708,0.00003251542,0.00036438575,0.00007438584,0.00031451744,0.00014335246],"domain_scores_gemma":[0.99875665,0.00042123502,0.00025504336,0.00008414072,0.00038541888,0.00009753077],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00026400184,0.000100506964,0.00014838595,0.00010710412,0.000052313775,0.00006106002,0.0002095863,0.000049900667,0.0069533912],"category_scores_gemma":[0.0002689316,0.000073163224,0.00010200082,0.000061894156,0.00009040139,0.0009062329,0.00007861232,0.00019579525,0.00017205202],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0003419561,0.0003555815,0.0049760067,0.000042756474,0.0006008376,0.000112225636,0.0011744269,0.00003567314,0.0005115648,0.5268423,0.023274088,0.44173256],"study_design_scores_gemma":[0.0006630453,0.00006519924,0.0043000667,0.00009521473,0.000024052826,0.001373617,0.0015298994,0.00006554149,0.00018864594,0.985205,0.0063761612,0.0001135394],"about_ca_topic_score_codex":0.0000019399167,"about_ca_topic_score_gemma":0.000001978636,"teacher_disagreement_score":0.4583627,"about_ca_system_score_codex":0.000053103384,"about_ca_system_score_gemma":0.000027165399,"threshold_uncertainty_score":0.99395436},"labels":[],"label_agreement":null},{"id":"W1989850648","doi":"10.1142/s1793042107001073","title":"ERRATUM: \"PRIME DIVISORS ARE POISSON DISTRIBUTED\"","year":2007,"lang":"en","type":"erratum","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Theories","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Poisson distribution; Prime (order theory); Prime minister; Prime number; Citation; Algebra over a field; Library science; Combinatorics; Discrete mathematics; Humanities; Statistics; Pure mathematics; Computer science; Philosophy; Law; Political science; Politics","score_opus":0.034581428804580594,"score_gpt":0.3647432683719428,"score_spread":0.3301618395673622,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1989850648","genre_codex":"other","genre_gemma":"other","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"other","genre_consensus":"other","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.0008191154,0.0021701572,0.4041254,0.0021540837,0.11524498,0.0006072507,0.004186726,0.00031665442,0.47037563],"genre_scores_gemma":[0.023816848,0.0014126489,0.075251415,0.0017497245,0.039000582,0.000045115798,0.0015280937,0.0010975227,0.85609806],"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9948367,0.0003096497,0.0018118095,0.00034608753,0.0021806967,0.000515096],"domain_scores_gemma":[0.9900465,0.0035729103,0.0035967242,0.00054648187,0.0019568764,0.00028053168],"candidate_categories":["metaresearch","metaepi_narrow","research_integrity","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002357738,0.0006344316,0.0012187274,0.00037135466,0.000090435584,0.00015720187,0.002031358,0.00069208245,0.00660067],"category_scores_gemma":[0.009738747,0.00052461197,0.00080006954,0.00021618896,0.0003533411,0.00041372972,0.00039790157,0.0024659876,0.00028481122],"study_design_candidate":"not_applicable","study_design_consensus":null,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00038095858,0.0003492439,0.00002062268,0.00010504442,0.00095801626,0.00074853183,0.00029480644,0.0000020783486,0.0000058637124,0.22756396,0.767837,0.0017339134],"study_design_scores_gemma":[0.00041292582,0.000039966464,0.00003541805,0.0016506977,0.00016602642,0.0008517284,0.00038925942,0.0000041135,0.00009711374,0.70083374,0.29516238,0.00035662783],"about_ca_topic_score_codex":0.0000011335705,"about_ca_topic_score_gemma":0.0000038196235,"teacher_disagreement_score":0.4732698,"about_ca_system_score_codex":0.0006154985,"about_ca_system_score_gemma":0.00026807998,"threshold_uncertainty_score":0.9998354},"labels":[],"label_agreement":null},{"id":"W1993793648","doi":"10.1142/s1793042111004009","title":"ORTHOGONAL SYSTEMS OF MODULAR FORMS AND SUPERSINGULAR POLYNOMIALS","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Concordia University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Modular form; Modulo; Prime (order theory); Modular design; Pure mathematics; Algebra over a field; Order (exchange); Eisenstein series; Product (mathematics); Discrete mathematics; Combinatorics; Computer science; Geometry","score_opus":0.03800595817072056,"score_gpt":0.2911574954047009,"score_spread":0.2531515372339803,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1993793648","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9814569,0.00027922288,0.0045390483,0.000028653474,0.00086216524,0.00007169202,0.00005457949,0.00001066904,0.012697116],"genre_scores_gemma":[0.99630433,0.000026627748,0.0028970796,0.000048650167,0.0002732104,0.000001682027,0.0000030239867,0.00002141369,0.00042398516],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99833906,0.00018130413,0.0007220157,0.00011148522,0.0004978178,0.00014833153],"domain_scores_gemma":[0.99801993,0.00060422433,0.0006330891,0.00015175661,0.00049013534,0.00010087747],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0017513753,0.0001423573,0.00035196857,0.00018029707,0.000033578235,0.00002231685,0.00042152373,0.00009277364,0.0017831303],"category_scores_gemma":[0.00055733084,0.000112188965,0.00018037061,0.00007220258,0.00017645238,0.00031431063,0.00008520091,0.00018326998,0.000013487793],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00073648314,0.00027114205,0.005723382,0.000056623856,0.0008926015,0.0001188533,0.0023079843,0.0000025332222,0.0013820507,0.9863098,0.0005159215,0.0016826213],"study_design_scores_gemma":[0.0009756549,0.00013846393,0.0028026877,0.0003055291,0.00011700755,0.0024008593,0.0021120997,0.00001257569,0.0046858285,0.985253,0.0010184671,0.00017783555],"about_ca_topic_score_codex":0.000007738623,"about_ca_topic_score_gemma":5.2548967e-7,"teacher_disagreement_score":0.014847473,"about_ca_system_score_codex":0.0000406737,"about_ca_system_score_gemma":0.000057456353,"threshold_uncertainty_score":0.99912935},"labels":[],"label_agreement":null},{"id":"W1994537091","doi":"10.1142/s1793042110003745","title":"THE FINITENESS OF COMPUTING THE ULTRAMETRIC MAHLER MEASURE","year":2010,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"advanced mathematical theories","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Simon Fraser University; University of British Columbia","funders":"","keywords":"Ultrametric space; Measure (data warehouse); Mathematics; Set (abstract data type); Computation; Algebraic number; Alpha (finance); Combinatorics; Open set; Discrete mathematics; Algorithm; Computer science; Mathematical analysis; Statistics; Metric space","score_opus":0.04775250674474802,"score_gpt":0.37662582556466245,"score_spread":0.32887331881991444,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1994537091","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.24071869,0.0012838747,0.6984664,0.0073452285,0.019344576,0.001113239,0.00044841826,0.000114152645,0.031165376],"genre_scores_gemma":[0.9599323,0.00011980393,0.03715603,0.0001399575,0.0015361609,0.000009367753,0.0000055391683,0.000077542245,0.0010232838],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9961767,0.00053261436,0.0014031652,0.00017750636,0.0014787278,0.0002312715],"domain_scores_gemma":[0.970854,0.023451805,0.0027388746,0.0006096779,0.0022764988,0.00006918467],"candidate_categories":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.005208944,0.00029776007,0.0005719869,0.00013957002,0.0001379413,0.00015479555,0.002798672,0.0002622916,0.000517709],"category_scores_gemma":[0.018090354,0.00015365795,0.0005557799,0.00016214233,0.00043784344,0.00010361338,0.0007629526,0.0021593517,0.000019225095],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00027749926,0.0002244933,0.00007706003,0.00011970003,0.0012720962,0.000031729804,0.0018085933,0.00027097375,0.0001492867,0.9728182,0.002167562,0.020782825],"study_design_scores_gemma":[0.00029509558,0.000016016296,0.000074989606,0.000721468,0.0001336645,0.0003619049,0.0006224818,0.00011971038,0.0009671057,0.99374956,0.0027809152,0.00015709712],"about_ca_topic_score_codex":0.0000024153603,"about_ca_topic_score_gemma":0.0000037145014,"teacher_disagreement_score":0.7192136,"about_ca_system_score_codex":0.00015776939,"about_ca_system_score_gemma":0.00021436722,"threshold_uncertainty_score":0.9901807},"labels":[],"label_agreement":null},{"id":"W1995158087","doi":"10.1142/s1793042110003848","title":"ON A CONJECTURE ON RAMANUJAN PRIMES","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":18,"is_retracted":false,"has_abstract":true,"route_ca_aff":false,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Ramanujan's sum; Mathematics; abc conjecture; Conjecture; Combinatorics; Prime (order theory); Upper and lower bounds; Integer (computer science); Discrete mathematics; Beal's conjecture; Mathematical analysis","score_opus":0.026577954160975692,"score_gpt":0.3763344848995317,"score_spread":0.349756530738556,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1995158087","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8319022,0.0000074348013,0.0020766826,0.0022315942,0.0022965355,0.00014356844,0.00005863397,0.00003881379,0.16124454],"genre_scores_gemma":[0.9888958,0.000003995637,0.0018378648,0.0007179306,0.0010487449,0.0000032198748,0.000004050129,0.000039483846,0.0074489084],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9977657,0.00023642994,0.00047302822,0.00015762872,0.0011550528,0.00021211692],"domain_scores_gemma":[0.9946575,0.003956785,0.00041509274,0.00029725602,0.00052405015,0.00014928661],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0018080677,0.00017813803,0.0002648363,0.00022027263,0.000051903186,0.00008765381,0.00096931786,0.000121560544,0.018807903],"category_scores_gemma":[0.003523288,0.0001297051,0.00025658158,0.0000805122,0.00016782084,0.00013042735,0.00007931111,0.001149663,0.00061231584],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0008998857,0.00037441196,0.0002677091,0.0000058497726,0.00040123184,0.00026501968,0.00031539987,0.000004636583,0.0006833192,0.95880336,0.033703618,0.0042755874],"study_design_scores_gemma":[0.00094780064,0.00014742276,0.00022239969,0.00012264523,0.000028052373,0.00078138936,0.00012045943,0.000018710263,0.0024323345,0.978525,0.016521685,0.00013212557],"about_ca_topic_score_codex":0.0000016356497,"about_ca_topic_score_gemma":0.000003752152,"teacher_disagreement_score":0.1569936,"about_ca_system_score_codex":0.000090415066,"about_ca_system_score_gemma":0.0001321965,"threshold_uncertainty_score":0.98208904},"labels":[],"label_agreement":null},{"id":"W1995360143","doi":"10.1142/s1793042112501035","title":"CONGRUENCES CONCERNING JACOBI POLYNOMIALS AND APÉRY-LIKE FORMULAE","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Dalhousie University","funders":"","keywords":"Congruence relation; Modulo; Theta function; Congruence (geometry); Algebra over a field","score_opus":0.047990952846653966,"score_gpt":0.3724591112072394,"score_spread":0.32446815836058546,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1995360143","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8735814,0.0012318679,0.037332863,0.0005828423,0.0030590198,0.00021412292,0.00008570191,0.000068420566,0.083843775],"genre_scores_gemma":[0.9804418,0.000059882543,0.015130807,0.0001847352,0.00078885636,0.0000036092993,0.0000015969063,0.00002211063,0.00336659],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9986298,0.00009655622,0.0005409403,0.00007293043,0.00045982024,0.00019992031],"domain_scores_gemma":[0.99679476,0.002125765,0.0005537809,0.000089528934,0.00030797833,0.00012816889],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0010413787,0.00012682278,0.00026600403,0.00008216861,0.000047722177,0.000072581686,0.00031671254,0.00005435376,0.0023669968],"category_scores_gemma":[0.0015235523,0.00010048417,0.00010418178,0.000033612174,0.00017243091,0.0009145698,0.000107839354,0.00018369782,0.000054162163],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00010998157,0.00013082106,0.0032768657,0.000037221056,0.00036685576,0.00003006206,0.0018601661,0.0000022431948,0.0007213639,0.98439854,0.0068454975,0.0022203506],"study_design_scores_gemma":[0.00053719425,0.000024318402,0.00040840532,0.00022304262,0.00006178905,0.0010013316,0.0024869943,0.000011688145,0.0013690395,0.984351,0.009379472,0.00014572953],"about_ca_topic_score_codex":0.0000031844463,"about_ca_topic_score_gemma":0.0000017339066,"teacher_disagreement_score":0.10686042,"about_ca_system_score_codex":0.000075534816,"about_ca_system_score_gemma":0.00003344199,"threshold_uncertainty_score":0.998545},"labels":[],"label_agreement":null},{"id":"W2003581098","doi":"10.1142/s1793042113500851","title":"REPRESENTATIONS BY CERTAIN OCTONARY QUADRATIC FORMS WHOSE COEFFICIENTS ARE 1, 2, 3 AND 6","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Pure mathematics; Quadratic equation; Binary quadratic form; Quadratic function; Geometry","score_opus":0.02981594313336515,"score_gpt":0.36405317042540597,"score_spread":0.3342372272920408,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2003581098","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.95555043,0.00016968521,0.019449066,0.0033933707,0.00047560758,0.00036723592,0.00014596553,0.000037254213,0.020411389],"genre_scores_gemma":[0.9883127,0.00003675383,0.0015765696,0.0003162227,0.00017659269,0.000016377606,0.000016257627,0.00003443902,0.009514085],"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9977574,0.00028382786,0.00065184006,0.00017174684,0.00090188783,0.00023331516],"domain_scores_gemma":[0.9961227,0.0020314958,0.00054913503,0.00021669574,0.0008853383,0.00019459715],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0010561702,0.00016076019,0.00027371335,0.00016326545,0.00008535459,0.0001626736,0.0006014444,0.000072342744,0.008067814],"category_scores_gemma":[0.001727171,0.00012495088,0.0001382301,0.00012182224,0.0002136787,0.00055769185,0.00016187644,0.00032394868,0.00025144118],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0006022676,0.0017757586,0.03994848,0.000097533884,0.0020583358,0.0003768914,0.0037118823,0.000026458709,0.0019820419,0.40969828,0.5238537,0.015868358],"study_design_scores_gemma":[0.0011146177,0.000053757798,0.002477586,0.00020006578,0.000053252414,0.0007822062,0.004022011,0.00042408193,0.00035764772,0.9868916,0.0034301565,0.00019298558],"about_ca_topic_score_codex":0.000020682992,"about_ca_topic_score_gemma":0.0000039483502,"teacher_disagreement_score":0.5771933,"about_ca_system_score_codex":0.000118964235,"about_ca_system_score_gemma":0.00006586147,"threshold_uncertainty_score":0.9928389},"labels":[],"label_agreement":null},{"id":"W2005983808","doi":"10.1142/s1793042115400035","title":"Primes in short arithmetic progressions","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Arithmetic progression; Moduli; Interval (graph theory); Prime (order theory); Prime number; Real number; Arithmetic function","score_opus":0.10417530276890707,"score_gpt":0.4378034742496684,"score_spread":0.33362817148076135,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2005983808","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.88684905,0.000235169,0.009284486,0.0020669503,0.0016081686,0.00030620676,0.000039802166,0.00005061635,0.09955955],"genre_scores_gemma":[0.98790395,0.000011847722,0.008790049,0.00009121315,0.00043032356,0.000007478768,0.0000036449026,0.000029447212,0.0027320504],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9974381,0.00039474867,0.00065507425,0.00012677102,0.001163185,0.00022216309],"domain_scores_gemma":[0.99734426,0.0011802948,0.00016437442,0.00018742861,0.0009149172,0.00020870099],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0034570692,0.00013044865,0.00027554997,0.00028613108,0.000019352576,0.00006062083,0.0008310538,0.00007360137,0.0017787084],"category_scores_gemma":[0.003519627,0.000101012396,0.00014311845,0.00017758064,0.00014755408,0.00027962588,0.00016512483,0.0004437128,0.000121436555],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0016695103,0.0019922962,0.08323187,0.000030282543,0.0009897813,0.0025297836,0.0045049246,0.00004031451,0.00021392723,0.81456685,0.0602202,0.030010285],"study_design_scores_gemma":[0.0008944207,0.000057643712,0.0010998243,0.00026642927,0.000028940554,0.0011598993,0.0012933766,0.00010177223,0.00041871387,0.9880567,0.0064909635,0.00013130151],"about_ca_topic_score_codex":0.000004421422,"about_ca_topic_score_gemma":0.0000067626033,"teacher_disagreement_score":0.17348988,"about_ca_system_score_codex":0.000275815,"about_ca_system_score_gemma":0.00033690082,"threshold_uncertainty_score":0.9991338},"labels":[],"label_agreement":null},{"id":"W2008792787","doi":"10.1142/s1793042112500030","title":"A GEOMETRIC VARIANT OF TITCHMARSH DIVISOR PROBLEM","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia; University of Lethbridge","funders":"","keywords":"Mathematics; Divisor (algebraic geometry); Abelian group; Abelian variety; Arithmetic of abelian varieties; Elliptic curve; Complex multiplication; Context (archaeology); Asymptotic formula; Division (mathematics); Variety (cybernetics); Riemann hypothesis; Pure mathematics; Abelian variety of CM-type; Distribution (mathematics); Elementary abelian group; Rank of an abelian group; Mathematical analysis; Arithmetic; Statistics","score_opus":0.04307174591986254,"score_gpt":0.2979189626522968,"score_spread":0.25484721673243427,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2008792787","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.67865914,0.0002473046,0.07598749,0.00019895297,0.0026203336,0.00026054512,0.00014699878,0.00005431782,0.24182494],"genre_scores_gemma":[0.9770005,0.000029808669,0.0207967,0.00010042992,0.00029215927,0.0000035952803,0.000003217625,0.000027611273,0.0017460027],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9979123,0.00022007005,0.000865096,0.00012643509,0.0006912076,0.00018487396],"domain_scores_gemma":[0.99668306,0.0011969286,0.0010339681,0.00020640314,0.00077799254,0.00010164006],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0021041923,0.00015906959,0.0003489261,0.0004455563,0.00002852361,0.000017611168,0.00086869043,0.00009212454,0.01755245],"category_scores_gemma":[0.0012782152,0.00012776522,0.00028537572,0.00034309874,0.00012452295,0.0002928589,0.00013920534,0.00027717958,0.00010780902],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0009683304,0.0012611331,0.003942188,0.00006502537,0.0014344756,0.00036878735,0.002861355,0.0000014837382,0.00024402002,0.96747524,0.0077990326,0.013578957],"study_design_scores_gemma":[0.0007844617,0.000113644826,0.0021473318,0.00017873695,0.00009299192,0.0012373821,0.0003858362,0.000002351403,0.0029998142,0.9895091,0.0024052928,0.00014304493],"about_ca_topic_score_codex":0.0000074709656,"about_ca_topic_score_gemma":7.06047e-7,"teacher_disagreement_score":0.29834133,"about_ca_system_score_codex":0.00005970989,"about_ca_system_score_gemma":0.00008748314,"threshold_uncertainty_score":0.9833456},"labels":[],"label_agreement":null},{"id":"W2010188103","doi":"10.1142/s179304211000368x","title":"EXACT AVERAGES OF CENTRAL VALUES OF TRIPLE PRODUCT L-FUNCTIONS","year":2010,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Triple product; Mathematics; Product (mathematics); Prime (order theory); Function (biology); Pure mathematics; Applied mathematics; Combinatorics; Geometry","score_opus":0.044748301079759786,"score_gpt":0.37064511540784256,"score_spread":0.32589681432808276,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2010188103","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.94485575,0.00029016775,0.019980611,0.0007606261,0.009281233,0.00053751824,0.001212018,0.000037993275,0.023044096],"genre_scores_gemma":[0.98191947,0.0001221137,0.0061071315,0.000019910889,0.0015509692,0.000007307123,0.000042000716,0.000064311986,0.010166765],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99541277,0.0006236708,0.001639978,0.00028674697,0.0017398989,0.00029693346],"domain_scores_gemma":[0.992067,0.0018512586,0.002544931,0.00063344045,0.0027477702,0.00015562044],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0034560545,0.00031007198,0.00087353674,0.00044746886,0.00003916546,0.000052428462,0.0017317662,0.00025949103,0.009997097],"category_scores_gemma":[0.005107893,0.0002598307,0.0008164902,0.00012482885,0.00044981,0.00019373608,0.00064186956,0.0018033866,0.000029603043],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0092860265,0.009130853,0.029433532,0.0027587821,0.027212974,0.00067780545,0.013145213,0.001639906,0.016987815,0.66998506,0.19274487,0.026997168],"study_design_scores_gemma":[0.0009105254,0.0000737028,0.0013421576,0.0009404318,0.00033746957,0.0004361879,0.00052101066,0.00012023096,0.009687352,0.98292667,0.0024530767,0.00025117988],"about_ca_topic_score_codex":0.000029424344,"about_ca_topic_score_gemma":0.000007383455,"teacher_disagreement_score":0.3129416,"about_ca_system_score_codex":0.00018963718,"about_ca_system_score_gemma":0.00072931574,"threshold_uncertainty_score":0.9999854},"labels":[],"label_agreement":null},{"id":"W2011044835","doi":"10.1142/s1793042108001249","title":"ON SOME CLASSES OF PERMUTATION POLYNOMIALS","year":2008,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":32,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University; University of Lethbridge","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Permutation (music); Combinatorics; Finite field; Cyclic permutation; Class (philosophy); Prime (order theory); Discrete mathematics; Symmetric group","score_opus":0.016238615781079935,"score_gpt":0.2759407172787741,"score_spread":0.2597021014976942,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2011044835","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9290521,0.00007999215,0.061028402,0.00059678534,0.0016662122,0.000034474193,0.000015339343,0.000022136486,0.0075045372],"genre_scores_gemma":[0.9967307,0.000032211214,0.002440532,0.00045951872,0.00020002408,8.467652e-7,0.0000012934845,0.0000051268858,0.00012973645],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99883705,0.00015895549,0.00035996886,0.000092577626,0.0004680219,0.000083406456],"domain_scores_gemma":[0.9983328,0.00072530116,0.00041412012,0.00013772454,0.00034313512,0.00004691397],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00054199534,0.00007768626,0.00013933054,0.00022194184,0.000041490697,0.000028517883,0.00089309434,0.000033493587,0.00040473577],"category_scores_gemma":[0.00021818599,0.00006525964,0.00018513114,0.000107629334,0.00009179186,0.00056191743,0.00006209944,0.00012375264,0.00003522377],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00021596783,0.0001535689,0.00060622307,0.0000019783981,0.00012644775,0.000083170424,0.0007216052,0.00009104155,0.0017145621,0.9839767,0.0022324587,0.010076274],"study_design_scores_gemma":[0.00061973056,0.0002294912,0.005525474,0.00009497519,0.000009268581,0.00094320596,0.000059736445,0.00008621192,0.008772172,0.98130745,0.00224186,0.000110429944],"about_ca_topic_score_codex":0.0000011387926,"about_ca_topic_score_gemma":1.3153004e-7,"teacher_disagreement_score":0.067678586,"about_ca_system_score_codex":0.000032322256,"about_ca_system_score_gemma":0.000080036916,"threshold_uncertainty_score":0.44315726},"labels":[],"label_agreement":null},{"id":"W2011541312","doi":"10.1142/s1793042111004058","title":"ON THE TRANSCENDENCE OF CERTAIN INFINITE SERIES","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Transcendental number; Mathematics; Transcendence (philosophy); Algebraic number; Series (stratigraphy); Pure mathematics; Combinatorics; Mathematical analysis","score_opus":0.09618202016839572,"score_gpt":0.35666527666849057,"score_spread":0.26048325650009485,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2011541312","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7544178,0.000048078808,0.017961813,0.002044238,0.0009774223,0.00023483949,0.00012134854,0.000028051732,0.22416645],"genre_scores_gemma":[0.99493515,0.000019183984,0.0015623483,0.00018204418,0.00013272096,0.000002970676,8.045557e-7,0.00001975334,0.0031450074],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99794775,0.00039758667,0.0005589438,0.00008663707,0.00086165906,0.00014744334],"domain_scores_gemma":[0.9955634,0.0029911792,0.00046439425,0.00022747439,0.0006915927,0.00006197135],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002258987,0.00011758459,0.00021288042,0.000119507364,0.000036214642,0.000019596779,0.0010610084,0.00005127129,0.017585123],"category_scores_gemma":[0.0019152692,0.0000726115,0.0002212949,0.00010685097,0.0003050898,0.00020362395,0.000056160934,0.00035247035,0.00008923191],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0011427301,0.00021655275,0.00074360124,0.000011215412,0.00043741553,0.00008070516,0.0028568506,0.000001951466,0.00023018714,0.9903011,0.0027715683,0.0012061746],"study_design_scores_gemma":[0.00031764375,0.00010459982,0.00039631175,0.00018477942,0.00003312952,0.00034362386,0.0011642686,0.0000088126935,0.004719622,0.99177223,0.0008811678,0.00007382907],"about_ca_topic_score_codex":0.000007319667,"about_ca_topic_score_gemma":0.000004779491,"teacher_disagreement_score":0.24051741,"about_ca_system_score_codex":0.00005004369,"about_ca_system_score_gemma":0.00009647364,"threshold_uncertainty_score":0.98331296},"labels":[],"label_agreement":null},{"id":"W2019048879","doi":"10.1142/s1793042112500042","title":"THE ITERATED INTEGRALS OF <font>ln</font>(1 + x<sup>n</sup>)","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Sequence (biology); Iterated function; Polynomial; Iterated function system; Algebra over a field","score_opus":0.052805217953281636,"score_gpt":0.3238724186236462,"score_spread":0.27106720067036455,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2019048879","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.70247453,0.00041462816,0.030306153,0.0012490822,0.0031682965,0.0004444496,0.00027135815,0.000071176255,0.2616003],"genre_scores_gemma":[0.9830422,0.000079217214,0.009197545,0.00020607252,0.0005530741,0.000009499905,0.000004858531,0.000036949004,0.0068705766],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99778646,0.00028817327,0.0011003545,0.00010055537,0.00054203154,0.00018240616],"domain_scores_gemma":[0.9951207,0.0027537583,0.0007943852,0.0002630402,0.00097197463,0.00009615949],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0019460334,0.0001659736,0.00034656463,0.00011258646,0.00007992766,0.00006102145,0.000800161,0.00008607118,0.010885166],"category_scores_gemma":[0.0022213992,0.00009790257,0.000316216,0.00010601102,0.00017243947,0.00021742315,0.00008590437,0.00029412765,0.00011531624],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0007062247,0.0004224199,0.00034291335,0.00002566934,0.00088998507,0.00004020301,0.0037877406,0.0000050982226,0.0001613112,0.94482154,0.041946664,0.006850252],"study_design_scores_gemma":[0.0006289415,0.00010206935,0.00013922181,0.00031475595,0.000096479234,0.00044577973,0.001292148,0.0001465684,0.0025544793,0.9705463,0.02359571,0.00013754146],"about_ca_topic_score_codex":0.000013689786,"about_ca_topic_score_gemma":0.0000040098585,"teacher_disagreement_score":0.28056765,"about_ca_system_score_codex":0.00005871937,"about_ca_system_score_gemma":0.00008622888,"threshold_uncertainty_score":0.990019},"labels":[],"label_agreement":null},{"id":"W2022312871","doi":"10.1142/s1793042110003174","title":"ON A CONJECTURE BY BOYD","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Conjecture; Identity (music); Measure (data warehouse); Beal's conjecture; Algebra over a field","score_opus":0.009675344771702092,"score_gpt":0.3269056601886808,"score_spread":0.3172303154169787,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2022312871","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8031537,0.000017046641,0.033521235,0.002788731,0.003060986,0.00012421032,0.00028917214,0.000034127006,0.15701082],"genre_scores_gemma":[0.99087906,0.0000044620097,0.005196781,0.0006318698,0.00037998878,0.0000019567574,0.000006137838,0.000021865852,0.0028778813],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99890924,0.000048891492,0.00037988325,0.000075391574,0.0004834682,0.000103114726],"domain_scores_gemma":[0.9975017,0.0016825321,0.00035412723,0.00012939058,0.00024710005,0.00008515181],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00065184984,0.00010428426,0.00017971346,0.00007586719,0.00002200039,0.00005507177,0.00043675886,0.000085392836,0.012529764],"category_scores_gemma":[0.0017558957,0.00007387933,0.00015107034,0.000039836683,0.000055180713,0.000088265515,0.000034497167,0.00048471018,0.00011703363],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00008151227,0.00024009387,0.000030666033,0.000005498484,0.00013208267,0.00004788949,0.00011592338,4.2494474e-7,0.0014902407,0.9332087,0.062466074,0.002180863],"study_design_scores_gemma":[0.0003885148,0.00003921641,0.000018366964,0.00005754781,0.000015977448,0.00045157486,0.000028971355,0.00008296961,0.0004461177,0.97288764,0.025502706,0.00008040633],"about_ca_topic_score_codex":5.605364e-7,"about_ca_topic_score_gemma":0.0000010627288,"teacher_disagreement_score":0.1877254,"about_ca_system_score_codex":0.000023302196,"about_ca_system_score_gemma":0.000028612161,"threshold_uncertainty_score":0.9883729},"labels":[],"label_agreement":null},{"id":"W2025059846","doi":"10.1142/s1793042109001943","title":"THE NUMBER OF REPRESENTATIONS OF A POSITIVE INTEGER BY CERTAIN QUATERNARY QUADRATIC FORMS","year":2009,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Integer (computer science); Quaternary; Quadratic equation; Pure mathematics; Function (biology); Combinatorics; Geometry","score_opus":0.017959334044688968,"score_gpt":0.3757487829235975,"score_spread":0.3577894488789085,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2025059846","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.760287,0.00028645518,0.14406079,0.004186811,0.0009978424,0.00047564955,0.00035359804,0.0000397532,0.089312114],"genre_scores_gemma":[0.988938,0.00005835923,0.0062199165,0.000089724075,0.00009826993,0.0000046749715,0.000007038483,0.000018958577,0.0045651034],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9977443,0.00017440783,0.0010942991,0.000095353156,0.00074378314,0.00014781066],"domain_scores_gemma":[0.99411625,0.0034833653,0.0012053731,0.00021613177,0.0009213929,0.000057501795],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007987702,0.00013901919,0.00032653267,0.0000689879,0.000050317394,0.000039274302,0.0006457138,0.000053258573,0.0008237957],"category_scores_gemma":[0.0020861882,0.00009044839,0.00026044436,0.000092716,0.00023578567,0.0004153658,0.000064832515,0.0002206761,0.000021242327],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00039464526,0.00048549444,0.00059053104,0.00002763806,0.00051681837,0.000031518484,0.0022303404,0.0000125802135,0.0019438335,0.982796,0.0095596295,0.0014109508],"study_design_scores_gemma":[0.00044397617,0.000060504823,0.00026503552,0.000331774,0.00006034485,0.00033219162,0.0022899597,0.0000667353,0.007220687,0.98867124,0.00017030915,0.00008724653],"about_ca_topic_score_codex":0.000009249774,"about_ca_topic_score_gemma":0.0000031265963,"teacher_disagreement_score":0.22865097,"about_ca_system_score_codex":0.00008322171,"about_ca_system_score_gemma":0.00005751718,"threshold_uncertainty_score":0.90199846},"labels":[],"label_agreement":null},{"id":"W2025620110","doi":"10.1142/s1793042105000303","title":"THE ILLUSORY SIEVE","year":2005,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Sieve (category theory); Dirichlet distribution; Prime (order theory); Discriminant; Elliptic curve; Pure mathematics; Combinatorics; Mathematical analysis; Artificial intelligence; Computer science","score_opus":0.039891150230699855,"score_gpt":0.3839993158497812,"score_spread":0.34410816561908136,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2025620110","genre_codex":"other","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.37046045,0.0010545147,0.04158518,0.037343,0.00544083,0.000501344,0.00013675723,0.0001474491,0.5433305],"genre_scores_gemma":[0.9603992,0.00011545218,0.004486327,0.00057806144,0.0025186136,0.0000047101953,0.0000019324643,0.00004141339,0.03185428],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99755794,0.00036195692,0.0006319236,0.00010266053,0.0011028952,0.00024260322],"domain_scores_gemma":[0.99373186,0.004541032,0.0004535273,0.00024755264,0.0009111369,0.000114915274],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0034964473,0.00012770426,0.00018520252,0.00008602662,0.00009786915,0.00011572422,0.0013402448,0.00005783447,0.0066793496],"category_scores_gemma":[0.0026878829,0.000079787824,0.00025488567,0.00008771173,0.00025339474,0.00028511143,0.00015571564,0.00044054078,0.0006128561],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000492495,0.00016503614,0.00031426936,0.0000036304118,0.0006844368,0.00009524858,0.00064395944,0.000012094194,0.0001220663,0.85512024,0.08929337,0.05305314],"study_design_scores_gemma":[0.00047234196,0.000021033537,0.00010793222,0.0000472284,0.000027930497,0.00080884364,0.00057994947,0.00006805846,0.0004054915,0.75500804,0.24236521,0.000087946675],"about_ca_topic_score_codex":0.0000013207837,"about_ca_topic_score_gemma":0.000007819791,"teacher_disagreement_score":0.58993876,"about_ca_system_score_codex":0.00021799955,"about_ca_system_score_gemma":0.00013900269,"threshold_uncertainty_score":0.99422866},"labels":[],"label_agreement":null},{"id":"W2026672820","doi":"10.1142/s1793042105000170","title":"LARGE SIEVE INEQUALITY WITH CHARACTERS FOR POWERFUL MODULI","year":2005,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"Harish-Chandra Research Institute","keywords":"Mathematics; Sieve (category theory); Moduli; Pure mathematics; Moduli space; Inequality; Combinatorics; Mathematical analysis","score_opus":0.043772129772810094,"score_gpt":0.3873838728906629,"score_spread":0.3436117431178528,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2026672820","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.83549386,0.00003634136,0.14765866,0.004486461,0.000570792,0.00033723426,0.0003230101,0.0000426382,0.011051022],"genre_scores_gemma":[0.98455,0.000008306389,0.008729568,0.00063114235,0.0011695147,0.00000797638,0.000016522263,0.000045908782,0.004841047],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9976902,0.00023106876,0.00065503566,0.00016819478,0.0009417522,0.00031374407],"domain_scores_gemma":[0.995769,0.0019480132,0.00060595677,0.0002306327,0.0012935979,0.00015278182],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0032143125,0.00017812055,0.00033145933,0.00014572726,0.00004266656,0.00007177846,0.00076769624,0.000075088414,0.004253123],"category_scores_gemma":[0.0013295698,0.00013206419,0.00024305894,0.0000907671,0.00010577246,0.0004562008,0.000088613255,0.00033730693,0.00014323546],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00443631,0.0011112876,0.0031468563,0.000045458815,0.0017930241,0.00012706083,0.0025946458,0.00002343314,0.00027791134,0.9624758,0.019389566,0.004578692],"study_design_scores_gemma":[0.003959784,0.00019783854,0.0008407311,0.00023695694,0.00011735898,0.0008896734,0.0013899883,0.00027689128,0.0014184507,0.9408117,0.04954275,0.00031785454],"about_ca_topic_score_codex":0.0000013141574,"about_ca_topic_score_gemma":0.000008807418,"teacher_disagreement_score":0.14905618,"about_ca_system_score_codex":0.00024028601,"about_ca_system_score_gemma":0.00015005945,"threshold_uncertainty_score":0.99665713},"labels":[],"label_agreement":null},{"id":"W2031023764","doi":"10.1142/s1793042110002879","title":"CONGRUENCES SATISFIED BY APÉRY-LIKE NUMBERS","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":42,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Mount Allison University","funders":"","keywords":"Mathematics; Congruence relation; Combinatorics; Pure mathematics; Arithmetic","score_opus":0.014676017823892155,"score_gpt":0.3456057596385875,"score_spread":0.3309297418146953,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2031023764","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.77733165,0.00011405481,0.038206782,0.0018327545,0.0113107925,0.00026875813,0.00029043478,0.0001402355,0.17050451],"genre_scores_gemma":[0.9418751,0.00003378649,0.040365435,0.00040564127,0.0007342999,0.000008066132,0.000009052883,0.000049150538,0.016519481],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99815905,0.00008423256,0.0006599276,0.00012214461,0.0007933495,0.00018128961],"domain_scores_gemma":[0.9964211,0.0020641196,0.00062555476,0.00017888716,0.00058774767,0.00012257764],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008106182,0.0001588151,0.00027824013,0.00008298418,0.000047594687,0.00010522656,0.0007707407,0.00009248662,0.01199178],"category_scores_gemma":[0.002248228,0.00013010665,0.00017725286,0.00006084766,0.00025903093,0.0005226122,0.00008603338,0.0004947132,0.00017784387],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00010685236,0.00022741569,0.0006884016,0.000021639955,0.00037593377,0.000097520555,0.00073642837,0.0000013442495,0.0055260453,0.84448624,0.14581701,0.0019151641],"study_design_scores_gemma":[0.00047581192,0.000018859035,0.00005999496,0.00007883046,0.000037108824,0.0006488535,0.0005620347,0.000008594769,0.0024513816,0.9746423,0.020873046,0.00014322512],"about_ca_topic_score_codex":0.000008749135,"about_ca_topic_score_gemma":0.000028559525,"teacher_disagreement_score":0.1645434,"about_ca_system_score_codex":0.000050152415,"about_ca_system_score_gemma":0.0000656657,"threshold_uncertainty_score":0.9889114},"labels":[],"label_agreement":null},{"id":"W2031876680","doi":"10.1142/s1793042108001213","title":"EFFECTIVE LOWER BOUND FOR THE VARIANCE OF DISTRIBUTION OF PRIMES IN ARITHMETIC PROGRESSIONS","year":2008,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Arithmetic; Variance (accounting); Upper and lower bounds; Distribution (mathematics); Order (exchange); Discrete mathematics; Mathematical analysis","score_opus":0.034891415555387766,"score_gpt":0.37986975885921,"score_spread":0.3449783433038222,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2031876680","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8772227,0.00026051508,0.11883867,0.00053641567,0.00062514,0.000693834,0.00025938364,0.000007440937,0.0015558812],"genre_scores_gemma":[0.9972918,0.000032654116,0.0019381159,0.000014422233,0.00014869,0.000025480746,0.000005750762,0.000014112331,0.0005289756],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99822426,0.00027840078,0.0006342675,0.00009396048,0.00062549696,0.00014359089],"domain_scores_gemma":[0.9914834,0.006580701,0.00065901096,0.0001674366,0.0010697278,0.000039712802],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0021617638,0.000099836434,0.00028772227,0.000090919944,0.000047742804,0.0000108281665,0.0005620372,0.00005740456,0.0004024111],"category_scores_gemma":[0.0036198439,0.00006497937,0.00022130164,0.00015454994,0.00041157065,0.00014015913,0.00007781604,0.00024061692,0.0000037160346],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.005253428,0.0027420167,0.022723615,0.00016102042,0.0020055443,0.00016271144,0.0029176746,0.00012575947,0.001418816,0.9436028,0.0081765605,0.010710046],"study_design_scores_gemma":[0.0018677841,0.00021503853,0.02146715,0.00064167136,0.00009756156,0.0005289893,0.00040673593,0.00042439034,0.003977785,0.9688921,0.0013689647,0.0001118214],"about_ca_topic_score_codex":0.0000071874238,"about_ca_topic_score_gemma":0.0000035576932,"teacher_disagreement_score":0.12006908,"about_ca_system_score_codex":0.00012929074,"about_ca_system_score_gemma":0.0001824215,"threshold_uncertainty_score":0.44061193},"labels":[],"label_agreement":null},{"id":"W2031940361","doi":"10.1142/s1793042114500134","title":"Binary theta series and modular forms with complex multiplication","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":true,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Modular form; Eisenstein series; Discriminant; Binary number; Series (stratigraphy); Character (mathematics); Galois module; Binary quadratic form; Integer (computer science); Space (punctuation); Pure mathematics; Theta function; Multiplication (music); Interpretation (philosophy); Quadratic equation; Combinatorics; Algebra over a field; Arithmetic; Quadratic function; Geometry","score_opus":0.02016997157291185,"score_gpt":0.3023030445695565,"score_spread":0.28213307299664464,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2031940361","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9804275,0.000044550434,0.014035615,0.0009837118,0.000087150605,0.00010161739,0.00001688321,0.000017064942,0.0042858957],"genre_scores_gemma":[0.9838333,0.000029167115,0.015052662,0.00014675045,0.00011706518,0.000006824906,0.0000072335733,0.000016049615,0.00079091056],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9992409,0.00003688602,0.0002615599,0.000081181526,0.00028774855,0.00009173298],"domain_scores_gemma":[0.9988285,0.00029171316,0.0003015416,0.00010606088,0.00041479032,0.000057424553],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0001966399,0.00009680252,0.00014271314,0.00007928128,0.000039181832,0.000047530004,0.00021666095,0.0000322587,0.0013569549],"category_scores_gemma":[0.00014293042,0.000062438696,0.000048268088,0.00005289248,0.00009411371,0.0006742896,0.000052626645,0.000121678,0.00003451843],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00064989115,0.0003263174,0.006433698,0.00003739997,0.00064884836,0.00006305212,0.00087532884,0.0000743118,0.0066687237,0.95863336,0.0030350406,0.022554016],"study_design_scores_gemma":[0.00056434784,0.00009031669,0.013047716,0.00007024445,0.000018518505,0.0009741801,0.00058406196,0.00010788807,0.000536054,0.98184353,0.0020653312,0.0000978097],"about_ca_topic_score_codex":0.0000010356652,"about_ca_topic_score_gemma":0.000001102936,"teacher_disagreement_score":0.02321016,"about_ca_system_score_codex":0.000029331599,"about_ca_system_score_gemma":0.000015468146,"threshold_uncertainty_score":0.99955595},"labels":[],"label_agreement":null},{"id":"W2033362684","doi":"10.1142/s1793042111004198","title":"SIMULTANEOUS ARITHMETIC PROGRESSIONS ON ALGEBRAIC CURVES","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Algebraic curve; Upper and lower bounds; Elliptic curve; Algebraic number; Arithmetic progression; Jacobian curve; Simple (philosophy); Stable curve","score_opus":0.018973637355927418,"score_gpt":0.27637134343375663,"score_spread":0.2573977060778292,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2033362684","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.21114302,0.0012357546,0.69621116,0.008442818,0.013643882,0.0004338371,0.00006087866,0.00032346576,0.06850517],"genre_scores_gemma":[0.9872346,0.00004304973,0.010484764,0.0015565521,0.00029019616,0.0000027067213,0.0000023773412,0.000008016058,0.00037775424],"study_design_codex":"design_other","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9987306,0.00013081872,0.00035753963,0.00013762062,0.00050897716,0.0001344518],"domain_scores_gemma":[0.99845505,0.0006010254,0.0003374041,0.00015212485,0.00035206391,0.000102344246],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004029328,0.00010799324,0.00013338406,0.00013484324,0.000042977306,0.0000590087,0.0012297622,0.000033081837,0.00078779773],"category_scores_gemma":[0.00039749342,0.00008225767,0.00012784814,0.00011772173,0.000054986474,0.00037104494,0.00013380982,0.00019621402,0.0001797605],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00025530235,0.00086812745,0.0004407966,0.000014366933,0.00033194592,0.001226741,0.0019833378,0.00012815563,0.000151712,0.47416028,0.009478499,0.51096076],"study_design_scores_gemma":[0.0014399252,0.00061268767,0.0054272846,0.0017056357,0.0000430503,0.0031820291,0.00009338742,0.0062134094,0.003654796,0.96189946,0.0152345495,0.00049375807],"about_ca_topic_score_codex":0.0000028699515,"about_ca_topic_score_gemma":5.928943e-7,"teacher_disagreement_score":0.7760916,"about_ca_system_score_codex":0.000047729318,"about_ca_system_score_gemma":0.000091934126,"threshold_uncertainty_score":0.8625833},"labels":[],"label_agreement":null},{"id":"W2042420699","doi":"10.1142/s179304211100499x","title":"A VARIANT OF THE BARBAN–DAVENPORT– HALBERSTAM THEOREM","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Class (philosophy); Prime (order theory); Extension (predicate logic); Congruence (geometry); Term (time); Square (algebra); Prime number; Norm (philosophy)","score_opus":0.038179591486679786,"score_gpt":0.28589438166935444,"score_spread":0.24771479018267464,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2042420699","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.6938667,0.00012931661,0.01556574,0.0005128103,0.0048381253,0.00023171201,0.00010955407,0.000034501732,0.2847115],"genre_scores_gemma":[0.99396354,0.000013289162,0.003310248,0.0002450301,0.00028934638,0.0000024238502,0.0000012851232,0.000027929473,0.0021469118],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99776304,0.00039111488,0.00081876444,0.00012327345,0.0007256615,0.00017813164],"domain_scores_gemma":[0.9966939,0.0011383123,0.0011370358,0.0003528987,0.0005948649,0.00008298652],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0022094944,0.000169234,0.00030512636,0.000117382864,0.00005120598,0.000017465256,0.0013268476,0.000095885094,0.014111637],"category_scores_gemma":[0.0014690199,0.00010713228,0.0004315916,0.00016391974,0.00029052712,0.00022562797,0.00018929722,0.00035402618,0.000048806425],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000536238,0.00038955314,0.0020738826,0.000015766647,0.000696186,0.00012695474,0.003845488,8.4124974e-7,0.0001498913,0.98708683,0.0034682667,0.0016100738],"study_design_scores_gemma":[0.000582377,0.000045989276,0.002179286,0.00019189314,0.00010475149,0.0016678644,0.00094827375,0.0000037336154,0.0048612957,0.98669815,0.0025981315,0.00011827386],"about_ca_topic_score_codex":0.000010070911,"about_ca_topic_score_gemma":0.0000021310614,"teacher_disagreement_score":0.3000968,"about_ca_system_score_codex":0.00006497224,"about_ca_system_score_gemma":0.00012458133,"threshold_uncertainty_score":0.9867896},"labels":[],"label_agreement":null},{"id":"W2048643528","doi":"10.1142/s1793042111004587","title":"SOME FOURTH-ORDER LINEAR DIVISIBILITY SEQUENCES","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":14,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Divisibility rule; Mathematics; Order (exchange); Class (philosophy); Combinatorics; Pure mathematics; Discrete mathematics; Computer science","score_opus":0.03145186301017809,"score_gpt":0.28481356452991613,"score_spread":0.253361701519738,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2048643528","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.28861427,0.00022653525,0.68956023,0.0007561897,0.0051423535,0.00007554393,0.000022680611,0.00009425361,0.015507966],"genre_scores_gemma":[0.9460326,0.0000352407,0.05268624,0.000496882,0.0005902869,0.0000016414895,9.869497e-7,0.0000070877622,0.0001490562],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99858403,0.00023296605,0.0003917552,0.00016567283,0.0004753887,0.00015015803],"domain_scores_gemma":[0.9984219,0.00031736807,0.00032764827,0.00025529607,0.0005833704,0.00009440396],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0014487538,0.00011285785,0.00014577738,0.00014758042,0.00005342622,0.00007326286,0.0019158465,0.000046469508,0.0014746627],"category_scores_gemma":[0.00024084667,0.00008946397,0.00020608929,0.0001695713,0.00012740765,0.0011202109,0.00021623884,0.00022699614,0.000098109136],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00017930975,0.0002365008,0.0064348127,0.000003160766,0.00026449858,0.00021048312,0.002655419,0.000019520434,0.00019020347,0.9614648,0.0005898202,0.02775143],"study_design_scores_gemma":[0.00030354195,0.000086803106,0.0045546833,0.000049246333,0.000010830043,0.0004308332,0.000085547166,0.00025967197,0.0014293183,0.9900076,0.0026518297,0.00013011153],"about_ca_topic_score_codex":0.0000060798566,"about_ca_topic_score_gemma":0.0000011776373,"teacher_disagreement_score":0.6574183,"about_ca_system_score_codex":0.000033134882,"about_ca_system_score_gemma":0.000085775464,"threshold_uncertainty_score":0.9994381},"labels":[],"label_agreement":null},{"id":"W2049731267","doi":"10.1142/s179304211100396x","title":"THE MULTIPLICATIVE ORDERS OF CERTAIN GAUSS FACTORIALS","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":9,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Dalhousie University","funders":"","keywords":"Mathematics; Multiplicative function; Combinatorics; Gauss sum; Multiplicative number theory; Prime (order theory); Congruence (geometry); Order (exchange); Gauss; Number theory; Multiplicative group; Prime number; Primitive root modulo n; Connection (principal bundle); Prime factor; Discrete mathematics; Mathematical analysis","score_opus":0.022330237245886408,"score_gpt":0.3144788778822457,"score_spread":0.2921486406363593,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2049731267","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.08620325,0.000060308917,0.7520243,0.00062304817,0.0013931062,0.00030046268,0.00036278652,0.000015367776,0.15901735],"genre_scores_gemma":[0.99547607,0.000006973318,0.0036848842,0.000019908419,0.0003240527,0.0000098653645,0.0000033871445,0.000008518324,0.00046634523],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9992338,0.000056881203,0.000378356,0.000056935587,0.00018849579,0.00008556701],"domain_scores_gemma":[0.9979863,0.00090265326,0.0005156137,0.00012214536,0.00043174595,0.000041538555],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00032796743,0.00007188049,0.00012799053,0.000017794859,0.000053043834,0.000013379225,0.00045270476,0.000015516973,0.002811074],"category_scores_gemma":[0.00010732556,0.000043930446,0.00012948341,0.00004582519,0.00015459029,0.00009656091,0.000047687678,0.00010489879,0.000026886692],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0001022857,0.00011029244,0.0005225709,9.591624e-7,0.00022902816,4.93413e-7,0.00065677095,0.000005022467,0.00032322068,0.9825616,0.00035123757,0.015136548],"study_design_scores_gemma":[0.00025107843,0.000015450398,0.00025743898,0.00002224824,0.00001633723,0.000003792844,0.0018873116,0.00000692014,0.005929365,0.9734473,0.018111926,0.000050786683],"about_ca_topic_score_codex":0.000010136397,"about_ca_topic_score_gemma":3.0034155e-7,"teacher_disagreement_score":0.9092728,"about_ca_system_score_codex":0.000014258662,"about_ca_system_score_gemma":0.000030115954,"threshold_uncertainty_score":0.9981005},"labels":[],"label_agreement":null},{"id":"W2050062132","doi":"10.1142/s1793042107001036","title":"ODD VALUES OF FOURIER COEFFICIENTS OF CERTAIN MODULAR FORMS","year":2007,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto; Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Modular form; Hecke operator; Coprime integers; Conjecture; Eigenvalues and eigenvectors; Pure mathematics; Siegel modular form; Fourier series; Operator (biology); Value (mathematics); Eisenstein series; Cusp form; Combinatorics; Mathematical analysis; Statistics","score_opus":0.019597968610999245,"score_gpt":0.3515327657404728,"score_spread":0.3319347971294736,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2050062132","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.78151983,0.000053297776,0.21302818,0.0000400967,0.00043733788,0.000042891974,0.000034607972,0.0000051061174,0.00483864],"genre_scores_gemma":[0.98783576,0.000011806419,0.011105412,0.00005556732,0.00018521327,3.5828077e-7,0.0000033211998,0.00001677853,0.00078580563],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9982001,0.000047166835,0.00076818565,0.00007518264,0.00076916354,0.00014016416],"domain_scores_gemma":[0.9971084,0.0009910555,0.0008771552,0.00013944067,0.00082113245,0.00006283407],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0014785363,0.00010232896,0.00026532332,0.00021904703,0.000017603077,0.000006932709,0.00043149234,0.000060274364,0.0010567775],"category_scores_gemma":[0.0011167055,0.00007872457,0.00021492623,0.00012571429,0.00010814648,0.00017990467,0.00006361933,0.00015461445,0.0000091765005],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0012856908,0.0011918881,0.0066205068,0.00008908203,0.00111,0.00015168737,0.0019552677,0.00048596904,0.00588431,0.93351555,0.0014432343,0.0462668],"study_design_scores_gemma":[0.00078462897,0.00007264083,0.0014638524,0.0001993801,0.00003781061,0.00013831952,0.00065593957,0.000057131998,0.02305177,0.9724371,0.0010141754,0.00008728329],"about_ca_topic_score_codex":8.320007e-7,"about_ca_topic_score_gemma":9.114878e-7,"teacher_disagreement_score":0.20631589,"about_ca_system_score_codex":0.000053945907,"about_ca_system_score_gemma":0.000037723155,"threshold_uncertainty_score":0.9998564},"labels":[],"label_agreement":null},{"id":"W2051279135","doi":"10.1142/s1793042115500803","title":"Construction of all cubic function fields of a given square-free discriminant","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Discriminant; Square (algebra); Mathematics; Cubic function; Finite field; Function (biology); Polynomial; Quadratic equation; Discriminant function analysis; Field (mathematics); Degree (music); Function field; Algebraic number field; Quadratic function; Pure mathematics; Discrete mathematics; Combinatorics; Mathematical analysis; Statistics; Geometry; Computer science; Artificial intelligence","score_opus":0.02506257259099395,"score_gpt":0.2749664585732548,"score_spread":0.24990388598226085,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2051279135","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.28425708,0.0001264929,0.70410544,0.0010045909,0.003425332,0.00005196849,0.00002371727,0.000017696322,0.0069877086],"genre_scores_gemma":[0.99123204,0.000013768157,0.008443719,0.00009270282,0.00016126812,0.0000010040882,0.0000019302902,0.000004292224,0.00004930105],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9987341,0.00016308937,0.00043352207,0.000092856804,0.0004941694,0.000082234656],"domain_scores_gemma":[0.9982007,0.00022493003,0.00057377695,0.0002249251,0.0007097895,0.00006584362],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008790987,0.00007865292,0.00016297234,0.00018872188,0.000013988124,0.000026129035,0.00097504805,0.000048458216,0.00017847317],"category_scores_gemma":[0.00022783667,0.00006495758,0.0001815471,0.00012504529,0.00011563274,0.0004419485,0.00015983434,0.00013340512,0.00000507484],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00077156007,0.00019286267,0.002029916,0.000012917918,0.00031853898,0.000024204852,0.002020798,0.000110374065,0.0008656944,0.94047374,0.003643376,0.049536046],"study_design_scores_gemma":[0.00093665527,0.00034797282,0.0015842535,0.00014216018,0.000042549145,0.00040388343,0.00057916786,0.00021777843,0.0033176797,0.9877979,0.0045414213,0.000088586465],"about_ca_topic_score_codex":0.000009660228,"about_ca_topic_score_gemma":0.0000025214958,"teacher_disagreement_score":0.7069749,"about_ca_system_score_codex":0.00003068254,"about_ca_system_score_gemma":0.000080279235,"threshold_uncertainty_score":0.26488933},"labels":[],"label_agreement":null},{"id":"W2052564373","doi":"10.1142/s179304210700081x","title":"A POLYNOMIAL ANALOGUE TO THE STERN SEQUENCE","year":2007,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"semigroups and automata theory","field":"Computer Science","cited_by":48,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Stern; Mathematics; Sequence (biology); Stirling number; Polynomial; Stirling numbers of the first kind; Stirling numbers of the second kind; Chebyshev polynomials; Mathematical proof; Simple (philosophy); Generating function; Combinatorics; Algebra over a field; Discrete mathematics; Pure mathematics; Mathematical analysis","score_opus":0.017536288150535276,"score_gpt":0.30942672289841205,"score_spread":0.2918904347478768,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2052564373","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.1613082,0.00007920645,0.8208603,0.006721915,0.0041353786,0.00007783604,0.000031718155,0.00004269918,0.006742697],"genre_scores_gemma":[0.98708296,0.0000059035915,0.006810161,0.00453269,0.0011009235,0.000001109529,0.0000016590426,0.000008018128,0.00045659684],"study_design_codex":"design_other","study_design_gemma":"not_applicable","domain_scores_codex":[0.9985513,0.00009812951,0.0004168566,0.00013540487,0.0005987815,0.00019953474],"domain_scores_gemma":[0.9983756,0.0006401607,0.00027442595,0.00026239903,0.0003265547,0.00012086492],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0025647148,0.00010233808,0.00011897467,0.00014103619,0.000056917364,0.0001811993,0.0027069529,0.00003584698,0.00030796035],"category_scores_gemma":[0.00021704836,0.00006674889,0.000132341,0.00018031712,0.000054899327,0.00045254652,0.00028218687,0.00020895417,0.0002363218],"study_design_candidate":"not_applicable","study_design_consensus":null,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00054675445,0.00023094972,0.0024624062,0.0000036686238,0.00046921213,0.0015444368,0.005520459,0.0002720707,0.0062900484,0.2626161,0.09350816,0.6265357],"study_design_scores_gemma":[0.0019986983,0.00035574194,0.030406987,0.00038160358,0.000043445358,0.011960178,0.0014147973,0.0019269154,0.011691629,0.14153409,0.79749554,0.0007903482],"about_ca_topic_score_codex":0.000012366967,"about_ca_topic_score_gemma":0.000012184191,"teacher_disagreement_score":0.8257747,"about_ca_system_score_codex":0.000100591664,"about_ca_system_score_gemma":0.00008063812,"threshold_uncertainty_score":0.50302374},"labels":[],"label_agreement":null},{"id":"W2053294172","doi":"10.1142/s1793042110003599","title":"SQUARE-FREE DISCRIMINANTS OF FROBENIUS RINGS","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Concordia University","funders":"Centre de Recherches Mathématiques","keywords":"Mathematics; Elliptic curve; Endomorphism; Algebraic number field; Complex multiplication; Pure mathematics; Rational number; Endomorphism ring; Square (algebra); Modulo; Ring of integers; Discriminant; Prime (order theory); Combinatorics; Discrete mathematics","score_opus":0.019603569530955014,"score_gpt":0.31838589004276574,"score_spread":0.29878232051181075,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2053294172","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9695389,0.000025998801,0.0038183678,0.00032639434,0.002736562,0.000059311384,0.00009150544,0.000018144165,0.023384761],"genre_scores_gemma":[0.9898377,0.0000096404565,0.007926723,0.0000964223,0.000683768,0.0000019076317,0.0000036534257,0.000028688051,0.0014114784],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.998078,0.00012175549,0.0007662065,0.00012368707,0.0007348649,0.00017547172],"domain_scores_gemma":[0.9964958,0.0014485474,0.00088878145,0.0003618627,0.0006975528,0.00010745053],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001542996,0.00016217005,0.0003294303,0.00018525709,0.00003729785,0.00003019758,0.0013435713,0.00011389699,0.009486789],"category_scores_gemma":[0.003241358,0.00013041263,0.0002915344,0.0001029435,0.00019798016,0.0003173371,0.0002108243,0.000512637,0.0000617263],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0007268691,0.00057333993,0.0076679587,0.000045341363,0.00054105505,0.00013585025,0.0015293326,0.0000012564993,0.005486273,0.96433467,0.0098877195,0.009070343],"study_design_scores_gemma":[0.0009916447,0.00004837676,0.0030272251,0.00014489226,0.00006914661,0.0009068438,0.0005120781,0.0000031599095,0.0141530605,0.9765081,0.0034985607,0.00013692067],"about_ca_topic_score_codex":0.000006415897,"about_ca_topic_score_gemma":0.0000067080537,"teacher_disagreement_score":0.021973282,"about_ca_system_score_codex":0.000030442903,"about_ca_system_score_gemma":0.000070882226,"threshold_uncertainty_score":0.99141866},"labels":[],"label_agreement":null},{"id":"W2054703906","doi":"10.1142/s1793042110003630","title":"ON CURIOUS GENERATING FUNCTIONS FOR VALUES OF L-FUNCTIONS","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Regina","funders":"","keywords":"Mathematics; Generating function; Series (stratigraphy); Pure mathematics; Function (biology); Algebra over a field; Mathematical analysis","score_opus":0.029789457177404804,"score_gpt":0.3680820945474183,"score_spread":0.33829263737001347,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2054703906","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.46903834,0.000024155997,0.5072764,0.00041023892,0.005062462,0.00019793911,0.00027143754,0.000040717183,0.017678306],"genre_scores_gemma":[0.8554448,0.000007923334,0.122644484,0.00015774785,0.0016824448,0.00002769894,0.000014063875,0.00005573453,0.01996509],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9987649,0.00004611815,0.0005814337,0.00008617159,0.00041388374,0.00010754622],"domain_scores_gemma":[0.9948944,0.0034277278,0.00056926336,0.00014854647,0.0009072002,0.000052889292],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00065067824,0.00010515214,0.00021105896,0.00012935775,0.000070961294,0.00003536494,0.00029407072,0.000057650028,0.0021646128],"category_scores_gemma":[0.005038053,0.00008639223,0.00023474477,0.0000466541,0.00010790976,0.00021740004,0.000038054284,0.00027251703,0.00003603744],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00014152178,0.0003443566,0.000041368396,0.000026518985,0.0002954725,0.000006180024,0.0003673164,0.00013060417,0.006500481,0.9704795,0.020035561,0.0016311484],"study_design_scores_gemma":[0.00046243457,0.00007515934,0.00002036052,0.00010680173,0.000064922795,0.00017515269,0.00037972326,0.0001934719,0.002074599,0.9937572,0.0026113116,0.00007889674],"about_ca_topic_score_codex":8.6630143e-7,"about_ca_topic_score_gemma":0.0000053277618,"teacher_disagreement_score":0.38640648,"about_ca_system_score_codex":0.000039765633,"about_ca_system_score_gemma":0.000055622684,"threshold_uncertainty_score":0.9987475},"labels":[],"label_agreement":null},{"id":"W2057027794","doi":"10.1142/s1793042112501163","title":"RECOGNIZING THE PRIMES USING PERMUTATIONS","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Brock University","funders":"","keywords":"Mathematics; Congruence (geometry); Combinatorics; Prime (order theory); Permutation (music); Integer (computer science); Statement (logic); Discrete mathematics; Set (abstract data type)","score_opus":0.020040947135924803,"score_gpt":0.2754748494102465,"score_spread":0.2554339022743217,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2057027794","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9535742,0.0009379047,0.018512193,0.000096268384,0.0057511553,0.000054477827,0.000025015583,0.00003984673,0.021008965],"genre_scores_gemma":[0.99822295,0.00001795167,0.0004937023,0.000072650764,0.0010437109,0.0000015641393,0.0000020774878,0.000016520173,0.00012885594],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9992352,0.0001176879,0.0002717106,0.000029909135,0.00022118728,0.00012427696],"domain_scores_gemma":[0.99930537,0.0003110016,0.00011186859,0.00006910149,0.00015170127,0.000050950443],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008267942,0.00007448094,0.00008673663,0.000067616864,0.00005229457,0.000041596955,0.00027900224,0.000031302974,0.00093783817],"category_scores_gemma":[0.00009158773,0.000051690684,0.00011157918,0.00006524782,0.000039510025,0.00037496808,0.00001745883,0.00016829385,0.00006420297],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00034760722,0.00042333605,0.0573925,0.000076611366,0.005486157,0.00012027796,0.034661323,0.027341595,0.032971002,0.74765503,0.02213622,0.07138832],"study_design_scores_gemma":[0.0030682075,0.000082691426,0.038701877,0.0015683083,0.0007079864,0.024401521,0.02645887,0.009792475,0.023604486,0.5147391,0.35521364,0.0016608128],"about_ca_topic_score_codex":0.0000011459605,"about_ca_topic_score_gemma":2.7388728e-7,"teacher_disagreement_score":0.3330774,"about_ca_system_score_codex":0.00005710683,"about_ca_system_score_gemma":0.000015258517,"threshold_uncertainty_score":0.99997544},"labels":[],"label_agreement":null},{"id":"W2058357075","doi":"10.1142/s1793042112500807","title":"ON NUMBER FIELDS WITH EQUIVALENT INTEGRAL TRACE FORMS","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; TRACE (psycholinguistics); Discriminant; Algebraic number field; Pure mathematics; Corollary; Signature (topology); Field (mathematics); Quartic function; Prime (order theory); Mathematical analysis; Combinatorics; Geometry","score_opus":0.02756779039632564,"score_gpt":0.32857276779915445,"score_spread":0.30100497740282883,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2058357075","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8851001,0.000047943042,0.02093819,0.0005603096,0.0016117991,0.00009347587,0.000029454866,0.000033914395,0.09158477],"genre_scores_gemma":[0.9915043,0.000011664521,0.0029334922,0.0005644075,0.0009451311,0.0000056755744,0.0000049270056,0.00003715219,0.0039932216],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99796575,0.00017965764,0.0005390883,0.000121827434,0.0008597791,0.00033390397],"domain_scores_gemma":[0.9969206,0.0017916689,0.0005201125,0.00021533099,0.0003573803,0.00019490147],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0015717879,0.00022693147,0.00029839066,0.00011632052,0.000056129596,0.0000481854,0.00060589885,0.000121690326,0.016632749],"category_scores_gemma":[0.0006972523,0.00014825126,0.00024672676,0.00011246367,0.00011042447,0.00058126514,0.00007217657,0.00057326,0.00042870452],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.001679549,0.00074954535,0.00450033,0.00001707101,0.000652145,0.0000884907,0.0015696205,0.0000072737157,0.0000203893,0.9701987,0.014713363,0.0058035557],"study_design_scores_gemma":[0.0012527159,0.000172692,0.0010035785,0.00029844747,0.000087070235,0.0027625067,0.0011212673,0.000003487632,0.0015000713,0.9814104,0.010134296,0.00025345534],"about_ca_topic_score_codex":0.000001724229,"about_ca_topic_score_gemma":0.0000012462084,"teacher_disagreement_score":0.106404185,"about_ca_system_score_codex":0.0001367323,"about_ca_system_score_gemma":0.000052556996,"threshold_uncertainty_score":0.98426616},"labels":[],"label_agreement":null},{"id":"W2067003407","doi":"10.1142/s1793042110002958","title":"THE TRANSCENDENCE OF SERIES RELATED TO STERN'S DIATOMIC SEQUENCE","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"semigroups and automata theory","field":"Computer Science","cited_by":16,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Stern; Sequence (biology); Transcendence (philosophy); Transcendental number; Mathematics; Series (stratigraphy); Power series; Generating function; Function (biology); Pure mathematics; Combinatorics; Mathematical analysis; Philosophy; Epistemology","score_opus":0.006925113414609191,"score_gpt":0.2767197288227818,"score_spread":0.2697946154081726,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2067003407","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9505919,0.00008510964,0.036345262,0.0050826264,0.005124528,0.00008383805,0.000034808396,0.000039532122,0.0026123507],"genre_scores_gemma":[0.99442,0.000037833634,0.0046533383,0.000267655,0.00011775364,0.0000020483842,6.6858235e-7,0.000007794949,0.0004929032],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9985997,0.000121210316,0.0004851047,0.0001215697,0.00053023564,0.00014214951],"domain_scores_gemma":[0.9981632,0.00067580835,0.00036406177,0.00029000928,0.00042379933,0.00008309964],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001351103,0.00009734607,0.00013518512,0.00007757036,0.00006071557,0.00012608296,0.0025596318,0.00004773309,0.00025534225],"category_scores_gemma":[0.0002826464,0.0000650642,0.0001286514,0.00013673947,0.00015580397,0.00068354997,0.00013650965,0.00031546515,0.000050361752],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00013447943,0.000050906358,0.00088155625,0.0000028175543,0.00012628392,0.0000821141,0.0017195354,0.00003509754,0.0436093,0.89452124,0.0006348471,0.058201823],"study_design_scores_gemma":[0.00070067623,0.00014332385,0.0074651507,0.000200094,0.000018313493,0.0036209265,0.0004511408,0.0007844921,0.040988747,0.92011607,0.025231475,0.00027960865],"about_ca_topic_score_codex":0.00000447541,"about_ca_topic_score_gemma":0.000006384708,"teacher_disagreement_score":0.057922218,"about_ca_system_score_codex":0.000028979754,"about_ca_system_score_gemma":0.00011294331,"threshold_uncertainty_score":0.47564754},"labels":[],"label_agreement":null},{"id":"W2069153442","doi":"10.1142/s1793042112500078","title":"EXPLICIT ZERO-FREE REGIONS FOR DEDEKIND ZETA FUNCTIONS","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Lethbridge","funders":"","keywords":"Zero (linguistics); Mathematics; Dedekind cut; Dedekind sum; Discriminant; Combinatorics; Function (biology); Field (mathematics); Degree (music); Simple (philosophy); Algebraic number field; Pure mathematics; Physics","score_opus":0.1418440441633517,"score_gpt":0.37843969831215557,"score_spread":0.23659565414880387,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2069153442","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.028296063,0.00006008491,0.84013,0.0011982308,0.0019542563,0.0003629278,0.0003511527,0.000063206135,0.12758411],"genre_scores_gemma":[0.9171887,0.000030509116,0.040446863,0.0003996181,0.0013599119,0.00005322014,0.000020214246,0.00010556741,0.040395405],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99790686,0.00019548768,0.0007041546,0.00017820107,0.0007324738,0.00028282605],"domain_scores_gemma":[0.995316,0.0021565743,0.0005436388,0.00045475116,0.0013519372,0.00017709035],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0018332159,0.00017735314,0.0002966651,0.0002454423,0.000106116204,0.000054401244,0.0014709441,0.000099737335,0.008737401],"category_scores_gemma":[0.003076442,0.00014917212,0.00043092587,0.00012601602,0.00014250977,0.00035151996,0.00020006788,0.00033854524,0.00019258281],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00074258045,0.00034037777,0.00039847515,0.000011270845,0.0008171342,0.00006528984,0.00094150763,9.358252e-7,0.00010132146,0.8560927,0.13927625,0.0012121645],"study_design_scores_gemma":[0.00120491,0.00008790085,0.00012892208,0.00010036841,0.00012653988,0.0008376895,0.0009088594,0.000024651603,0.00049386965,0.97487515,0.021063473,0.00014765217],"about_ca_topic_score_codex":0.00000771137,"about_ca_topic_score_gemma":0.000010096185,"teacher_disagreement_score":0.88889265,"about_ca_system_score_codex":0.00015214185,"about_ca_system_score_gemma":0.00015172383,"threshold_uncertainty_score":0.9921687},"labels":[],"label_agreement":null},{"id":"W2069420780","doi":"10.1142/s1793042110003617","title":"THE RAMIFICATION GROUPS AND DIFFERENT OF A COMPOSITUM OF ARTIN–SCHREIER EXTENSIONS","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Degree (music); Galois group; Function field; Field (mathematics); Algebraic number field; Pure mathematics; Genus; Divisor (algebraic geometry); Ideal (ethics); Combinatorics; Ramification; Constant (computer programming); Discrete mathematics; Botany","score_opus":0.014755654619398388,"score_gpt":0.30200004482434706,"score_spread":0.2872443902049487,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2069420780","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9934822,0.00006546509,0.003409743,0.00047973066,0.00083319284,0.00006584966,0.000021383938,0.0000054033494,0.0016370544],"genre_scores_gemma":[0.99810463,0.000044913304,0.0013336589,0.000032705888,0.00018535658,0.000002126543,0.0000026198313,0.000011948107,0.0002820607],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9985497,0.00016986755,0.0006663322,0.00008083503,0.00043410275,0.000099136865],"domain_scores_gemma":[0.9954362,0.0027714812,0.0008818535,0.00020320542,0.00064575125,0.00006151679],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001306536,0.00010379206,0.00023075998,0.00008400551,0.000064980566,0.000021576521,0.00041781933,0.00006408147,0.00052285014],"category_scores_gemma":[0.0011436256,0.00006487679,0.0001434335,0.00006264002,0.00031707907,0.000114848626,0.00009204575,0.0003266012,0.000004682426],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00046724762,0.00032087276,0.0037074091,0.000018996941,0.00034246317,0.000007558157,0.00074099196,0.0000010411613,0.039246403,0.948838,0.00078138645,0.0055276067],"study_design_scores_gemma":[0.00059210375,0.00005075256,0.02239065,0.00010994231,0.00007479896,0.00044492783,0.00059010636,0.00003730697,0.017101837,0.9576039,0.0009242992,0.00007941529],"about_ca_topic_score_codex":0.0000013744756,"about_ca_topic_score_gemma":0.0000032026094,"teacher_disagreement_score":0.022144565,"about_ca_system_score_codex":0.000012668998,"about_ca_system_score_gemma":0.000028422564,"threshold_uncertainty_score":0.5724842},"labels":[],"label_agreement":null},{"id":"W2072320355","doi":"10.1142/s1793042112501047","title":"NON-COMMUTATIVE p-ADIC L-FUNCTIONS FOR SUPERSINGULAR PRIMES","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"McGill University","funders":"Monash University","keywords":"Mathematics; Supersingular elliptic curve; Elliptic curve; Galois module; Abelian extension; Extension (predicate logic); Pure mathematics; Conjecture; Abelian group; Galois group; Commutative property; Discrete mathematics; Algebra over a field","score_opus":0.029629907741759602,"score_gpt":0.3401392172445643,"score_spread":0.3105093095028047,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2072320355","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7784168,0.00030741666,0.18814752,0.00078129757,0.0055265822,0.00029093772,0.00018911196,0.000044152614,0.026296169],"genre_scores_gemma":[0.9839592,0.0000076156844,0.010588942,0.00027460538,0.001598595,0.000012001263,0.000018526789,0.000033668817,0.0035068549],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99859446,0.00014777198,0.0004951153,0.000090932146,0.0004158948,0.0002558235],"domain_scores_gemma":[0.99633026,0.0023329374,0.0004222608,0.00015102215,0.0006237057,0.00013980585],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0019554277,0.00015609933,0.00026179856,0.00016957654,0.000104414656,0.00003644602,0.00045390756,0.00008402643,0.0038552997],"category_scores_gemma":[0.0013020012,0.00013155803,0.0003298756,0.0000966734,0.00012308962,0.0005477614,0.00006094726,0.00025536076,0.00012571532],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0016938846,0.0016441453,0.008012879,0.00006420618,0.0031243241,0.000035788224,0.012683495,0.000014256182,0.0010197498,0.8639261,0.09797763,0.00980352],"study_design_scores_gemma":[0.0013318943,0.00009566555,0.000992767,0.00014574609,0.00019711306,0.0009695758,0.004120639,0.00001450251,0.003780137,0.9485966,0.039536513,0.00021886303],"about_ca_topic_score_codex":0.0000013657756,"about_ca_topic_score_gemma":2.4043442e-7,"teacher_disagreement_score":0.20554237,"about_ca_system_score_codex":0.0001282723,"about_ca_system_score_gemma":0.00007461162,"threshold_uncertainty_score":0.9970553},"labels":[],"label_agreement":null},{"id":"W2075072737","doi":"10.1142/s1793042107000778","title":"PRIME DIVISORS ARE POISSON DISTRIBUTED","year":2007,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Poisson distribution; Prime (order theory); Prime factor; Integer (computer science); Set (abstract data type); Combinatorics; Distribution (mathematics); Almost prime; Prime number; Discrete mathematics; Statistics; Computer science; Mathematical analysis","score_opus":0.04250197517674684,"score_gpt":0.3856569694398367,"score_spread":0.3431549942630898,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2075072737","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.65972614,0.00012307454,0.29745564,0.0018706999,0.0018650097,0.00021276493,0.0003025499,0.00008566887,0.038358457],"genre_scores_gemma":[0.99321157,0.0000122551455,0.0026824363,0.00015231447,0.00081858237,0.0000012783436,0.000015467527,0.000038316197,0.0030677873],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9971641,0.00023877746,0.0008045473,0.00015018944,0.0013079761,0.0003344471],"domain_scores_gemma":[0.994901,0.0026601332,0.00083113933,0.00023728199,0.0011598767,0.00021055795],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0046213483,0.00017404635,0.00031769834,0.00021630216,0.000056600282,0.00007157693,0.0010093687,0.00010030465,0.007713356],"category_scores_gemma":[0.0034703724,0.00014283435,0.00028416197,0.00018167065,0.000156325,0.0002667288,0.00016437056,0.00049261795,0.00024233031],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0052663935,0.001903467,0.048352864,0.00005485815,0.0033701183,0.003867655,0.0020227325,0.000015761594,0.0011002524,0.817316,0.085120715,0.031609163],"study_design_scores_gemma":[0.0011774385,0.00005356356,0.008175148,0.0002532804,0.00007135093,0.0012785937,0.0013526204,0.000025884365,0.0033579245,0.96575034,0.01827823,0.00022562536],"about_ca_topic_score_codex":0.0000032400014,"about_ca_topic_score_gemma":0.0000060191314,"teacher_disagreement_score":0.33348542,"about_ca_system_score_codex":0.00031219455,"about_ca_system_score_gemma":0.000089465204,"threshold_uncertainty_score":0.99319375},"labels":[],"label_agreement":null},{"id":"W2083525726","doi":"10.1142/s1793042111004010","title":"THE FRACTIONAL GALOIS IDEAL FOR ARBITRARY ORDER OF VANISHING","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Ideal (ethics); Mathematics; Abelian extension; Fractional ideal; Order (exchange); Extension (predicate logic); Ideal class group; Class (philosophy); Abelian group; Simple (philosophy); Group (periodic table); Galois group; Pure mathematics; Discrete mathematics; Algebra over a field; Algebraic number field; Combinatorics; Law; Computer science","score_opus":0.04544400079900817,"score_gpt":0.3250887261032002,"score_spread":0.27964472530419204,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2083525726","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.5832685,0.0005249775,0.27703235,0.001431342,0.00885772,0.00051350344,0.00032323838,0.000066956934,0.1279814],"genre_scores_gemma":[0.9720795,0.000041685606,0.025445176,0.00027855666,0.00085837726,0.000009958473,0.000006197357,0.000033718836,0.0012467909],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99827564,0.0001644123,0.00072970736,0.00010105559,0.0005616843,0.00016751286],"domain_scores_gemma":[0.99323136,0.0045349146,0.00089379534,0.00015733023,0.0011167562,0.00006586349],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0023539483,0.0001250695,0.00022035638,0.00008937883,0.00010774803,0.00003243421,0.0007515751,0.00007918368,0.0031168158],"category_scores_gemma":[0.0023801704,0.00009003261,0.00028337986,0.000095916344,0.00016234825,0.0003474114,0.000070169845,0.00029403545,0.000021284597],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0014984232,0.0002518954,0.00079664675,0.000017329783,0.0008525869,0.000020713935,0.0011716393,0.0000018260015,0.00013892633,0.9809282,0.008557784,0.005764031],"study_design_scores_gemma":[0.00063041423,0.0000628118,0.0010137879,0.000081238075,0.00006196256,0.00043655955,0.00097277097,0.000011460427,0.002257663,0.98374164,0.010632987,0.00009672487],"about_ca_topic_score_codex":0.000005480311,"about_ca_topic_score_gemma":0.0000024555045,"teacher_disagreement_score":0.388811,"about_ca_system_score_codex":0.000051380062,"about_ca_system_score_gemma":0.00013085137,"threshold_uncertainty_score":0.99779445},"labels":[],"label_agreement":null},{"id":"W2091416417","doi":"10.1142/s1793042109002602","title":"A GENERALIZATION OF ROTH'S THEOREM IN FUNCTION FIELDS","year":2009,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":5,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Cardinality (data modeling); Combinatorics; Generalization; Degree (music); Finite field; Polynomial; Ring (chemistry); Zero (linguistics); Polynomial ring; Field (mathematics); Discrete mathematics; Function field; Function (biology); Pure mathematics; Mathematical analysis","score_opus":0.008158623682477266,"score_gpt":0.25729639132960014,"score_spread":0.24913776764712287,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2091416417","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.13918482,0.0000797417,0.8503323,0.00078093004,0.0009570866,0.00003620507,0.000002250632,0.000015189116,0.008611449],"genre_scores_gemma":[0.99571776,0.000021373846,0.0034451985,0.0005973037,0.00015796306,5.999174e-7,0.0000015003242,0.000002638112,0.00005565918],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99902874,0.00015704431,0.00035086868,0.00008372448,0.00030191973,0.0000776875],"domain_scores_gemma":[0.999152,0.00015033915,0.00028293912,0.000122394,0.00026325238,0.000029089691],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000803145,0.000065837216,0.00011148975,0.00023749133,0.000014920842,0.000039420094,0.0006646874,0.000044406825,0.00033299797],"category_scores_gemma":[0.000090640926,0.00005673875,0.000114957555,0.00021452799,0.000026501966,0.00043219796,0.000035666384,0.00012097903,0.000005056261],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00019818664,0.000111145586,0.0010157863,0.0000012271772,0.000036395435,0.000018722949,0.0004824968,0.0004040303,0.0005594263,0.910068,0.00041850313,0.08668611],"study_design_scores_gemma":[0.00045319975,0.00014117696,0.010658825,0.0000757329,0.0000059781387,0.00010395904,0.00003801936,0.0006802196,0.0012815369,0.9851679,0.0013248723,0.00006856687],"about_ca_topic_score_codex":0.00000186231,"about_ca_topic_score_gemma":0.0000015211696,"teacher_disagreement_score":0.85653293,"about_ca_system_score_codex":0.000025853318,"about_ca_system_score_gemma":0.00003517422,"threshold_uncertainty_score":0.36460942},"labels":[],"label_agreement":null},{"id":"W2091740811","doi":"10.1142/s1793042109002225","title":"REDUCTION modp OF SUBGROUPS OF THE MORDELL–WEIL GROUP OF AN ELLIPTIC CURVE","year":2009,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto; University of Lethbridge","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Combinatorics; Elliptic curve; Good reduction; Cardinality (data modeling); Modulo; Prime (order theory); Divisor (algebraic geometry); Reduction (mathematics); Zero (linguistics); Rank (graph theory); Prime factor; Group (periodic table); Algebraic number field; Function field; Discrete mathematics; Field (mathematics); Arithmetic; Pure mathematics; Geometry","score_opus":0.019037122679168225,"score_gpt":0.3025210716685285,"score_spread":0.28348394898936025,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2091740811","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9911905,0.00009243805,0.003437071,0.00017211403,0.0009457219,0.00009083209,0.00004199086,0.000007421374,0.0040219184],"genre_scores_gemma":[0.996701,0.000030160767,0.0024653764,0.0000433641,0.0003619549,8.4701713e-7,0.000004550509,0.000016330981,0.0003763963],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9974849,0.00040116315,0.0010459964,0.0001174028,0.00081891526,0.00013161532],"domain_scores_gemma":[0.9965787,0.0005644816,0.0016762653,0.00032139273,0.0007992624,0.000059909882],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001861102,0.00014994762,0.0003837023,0.00016788747,0.000029614954,0.0000099817835,0.00088027155,0.000098608325,0.0010199054],"category_scores_gemma":[0.000592193,0.00010854941,0.00034323928,0.00021768334,0.00023504518,0.0003426812,0.00005945174,0.0002836684,0.000004383502],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.002219129,0.0021927427,0.0010609638,0.00008633385,0.0007480572,0.000017896435,0.0030606466,0.00024124514,0.027588595,0.94858354,0.0007758962,0.013424932],"study_design_scores_gemma":[0.00077657006,0.00023886569,0.004141473,0.00029463682,0.00010916021,0.00054892927,0.0010025383,0.000065570275,0.032863148,0.95970565,0.00014412201,0.000109340195],"about_ca_topic_score_codex":0.000007376566,"about_ca_topic_score_gemma":0.0000011068707,"teacher_disagreement_score":0.013315592,"about_ca_system_score_codex":0.000056216257,"about_ca_system_score_gemma":0.000065505345,"threshold_uncertainty_score":0.9998933},"labels":[],"label_agreement":null},{"id":"W2092272088","doi":"10.1142/s1793042111004733","title":"MULTIPLE PATTERNS OF k-TUPLES OF INTEGERS","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Iterated function; Sequence (biology); Variety (cybernetics); Integer sequence; Tuple; Arithmetic; Fibonacci number; Combinatorics; Discrete mathematics; Generating function","score_opus":0.06953871921737875,"score_gpt":0.3408957478540114,"score_spread":0.27135702863663264,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2092272088","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8517658,0.000048308717,0.1278923,0.000044308494,0.0008073471,0.00009281857,0.0001594038,0.00001629388,0.01917343],"genre_scores_gemma":[0.9709647,0.00002569022,0.028103653,0.000017420543,0.00008900035,0.0000017406853,0.000001591337,0.000019356145,0.0007767981],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9984539,0.00007778484,0.0008212241,0.00006596788,0.00048518588,0.00009594958],"domain_scores_gemma":[0.99658424,0.001450462,0.0010261406,0.00014608653,0.000745816,0.00004725766],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.000536388,0.00010245083,0.0003110614,0.00013082668,0.000009265053,0.000006542361,0.00054882927,0.00004551418,0.004379618],"category_scores_gemma":[0.0021686812,0.000081568265,0.00021989316,0.000039195802,0.00013213661,0.00024917154,0.00009404526,0.0001426062,0.000013387071],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0004686695,0.0007958659,0.015057606,0.00019381782,0.00082303485,0.000066816814,0.0059491885,0.000007423301,0.0023471783,0.9716183,0.0010102044,0.0016618961],"study_design_scores_gemma":[0.00047431016,0.00004868355,0.0010621249,0.0004847809,0.00004823691,0.00013496088,0.0020989988,0.000015362924,0.03248445,0.9629472,0.0001254059,0.00007552339],"about_ca_topic_score_codex":0.000012051193,"about_ca_topic_score_gemma":0.000007076342,"teacher_disagreement_score":0.119198956,"about_ca_system_score_codex":0.000039253595,"about_ca_system_score_gemma":0.00003432812,"threshold_uncertainty_score":0.99653053},"labels":[],"label_agreement":null},{"id":"W2093579744","doi":"10.1142/s179304211250159x","title":"A NOTE ON BARKER POLYNOMIALS","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Mathematics; Degree (music); Combinatorics; Polynomial; Irreducibility; Integer (computer science); Discrete mathematics; Pure mathematics","score_opus":0.042224918793121534,"score_gpt":0.37000400926845156,"score_spread":0.32777909047533005,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2093579744","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.49034318,0.00018049254,0.044919226,0.0030801857,0.012821782,0.00029472666,0.00023168993,0.000080410806,0.44804832],"genre_scores_gemma":[0.98079485,0.000010157571,0.010148497,0.00091678096,0.0030498651,0.000004893887,0.000002707182,0.000030159299,0.0050420896],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9984732,0.00017848355,0.00058567256,0.0000668335,0.00050045724,0.00019532989],"domain_scores_gemma":[0.99613243,0.002898477,0.0004122922,0.00016028539,0.00024317387,0.00015331419],"candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0017276038,0.0001283284,0.00024819814,0.00011931861,0.00003681613,0.0000414521,0.00033929606,0.00007332964,0.024212891],"category_scores_gemma":[0.002183179,0.00009256217,0.00023652827,0.00005133326,0.000044443743,0.00024568744,0.00004649583,0.00021552187,0.00078808714],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0004661375,0.0006299293,0.0004875753,0.0000125444785,0.0003433898,0.000019156767,0.00075138774,0.0000016141599,0.00064659806,0.84866816,0.13838647,0.00958706],"study_design_scores_gemma":[0.0008800559,0.00009734834,0.000625666,0.0002438593,0.000095813164,0.0008362134,0.00016719404,0.000009203458,0.0031288115,0.760757,0.23293948,0.00021931838],"about_ca_topic_score_codex":0.0000011106152,"about_ca_topic_score_gemma":2.9230358e-7,"teacher_disagreement_score":0.49045166,"about_ca_system_score_codex":0.00009534294,"about_ca_system_score_gemma":0.00004294592,"threshold_uncertainty_score":0.9999899},"labels":[],"label_agreement":null},{"id":"W2096027073","doi":"10.1142/s1793042112500571","title":"RATIONAL EQUIVARIANT FORMS","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":17,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Ottawa; Université de Montréal; Concordia University","funders":"","keywords":"Equivariant map; Mathematics; Pure mathematics; Modular form; Modular curve; Modular design; Action (physics); Upper half-plane; Algebra over a field; Parametrization (atmospheric modeling); Computer science","score_opus":0.03300275658279919,"score_gpt":0.34390022307872664,"score_spread":0.3108974664959274,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2096027073","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.87074584,0.00023974909,0.052090645,0.0011872664,0.016124165,0.00014780951,0.00005421603,0.000043777538,0.05936656],"genre_scores_gemma":[0.99356365,0.0000067867354,0.0032131223,0.0002481268,0.0024041687,0.0000021954422,0.0000043642262,0.000015476513,0.00054211996],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9986933,0.00006934952,0.00041164807,0.000053869255,0.0006099761,0.00016189163],"domain_scores_gemma":[0.9985063,0.0005617582,0.00037677772,0.000094423754,0.00035918516,0.000101536214],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007488455,0.00009818906,0.00015137072,0.00006185484,0.000035637833,0.000039003113,0.00039356342,0.000058890517,0.006595837],"category_scores_gemma":[0.0005329361,0.00007106456,0.0001621972,0.000040245737,0.000036513342,0.0004722993,0.000069333466,0.00017331597,0.00004851945],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00013401727,0.00010292493,0.0007264224,0.000002473386,0.00021863224,0.000009556095,0.00038898355,0.0000025618701,0.00006043016,0.991584,0.00519993,0.0015700433],"study_design_scores_gemma":[0.0004986611,0.000018802057,0.00070658437,0.000030168256,0.000025701533,0.0005917573,0.0001221029,0.0000062269337,0.00030784495,0.98458976,0.013018725,0.00008369196],"about_ca_topic_score_codex":9.0445366e-7,"about_ca_topic_score_gemma":2.31898e-7,"teacher_disagreement_score":0.12281783,"about_ca_system_score_codex":0.00009008974,"about_ca_system_score_gemma":0.00006198843,"threshold_uncertainty_score":0.9943123},"labels":[],"label_agreement":null},{"id":"W2096827029","doi":"10.1142/s1793042108001705","title":"UNDECIDABILITY OF FAMILIES OF RINGS OF TOTALLY REAL INTEGERS","year":2008,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Royal College of Physicians and Surgeons of Canada; Mount Royal University","funders":"Tel Aviv University; Minerva Foundation; American Institute of Mathematics","keywords":"Mathematics; Undecidable problem; Integer (computer science); Ring (chemistry); Combinatorics; Order (exchange); Ring of integers; Group ring; Discrete mathematics; Pure mathematics; Group (periodic table); Algebraic number field","score_opus":0.030548067021777134,"score_gpt":0.31551354589098424,"score_spread":0.2849654788692071,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2096827029","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.95962185,0.000033713302,0.002285594,0.000053588265,0.0004168324,0.000060698247,0.00006482029,0.0000074303666,0.037455495],"genre_scores_gemma":[0.9956114,0.00010148689,0.0036543154,0.000022068285,0.00011281141,0.0000010935823,0.000002642928,0.000016029619,0.00047815207],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99752074,0.00022371368,0.0012341173,0.00010939168,0.00078932045,0.00012268341],"domain_scores_gemma":[0.99465704,0.002321651,0.0014854106,0.00022952339,0.001243461,0.000062918065],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0016299755,0.00014128603,0.0005095637,0.00021852429,0.00002156332,0.0000037252858,0.0006606786,0.00009112721,0.0020093822],"category_scores_gemma":[0.0018873158,0.00011840006,0.00037203796,0.00016285972,0.000581384,0.00021575701,0.00011619595,0.00022853442,0.0000062976396],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0032461076,0.0016190436,0.041883457,0.00025531612,0.0018139961,0.00009452874,0.008547757,0.000053461074,0.010080289,0.92657334,0.0020200666,0.0038126144],"study_design_scores_gemma":[0.0010102023,0.00018246469,0.017530177,0.00034347503,0.000072789495,0.0005911633,0.002422563,0.0000063855273,0.048798878,0.9287008,0.000207918,0.00013319167],"about_ca_topic_score_codex":0.00003010031,"about_ca_topic_score_gemma":0.0000030069252,"teacher_disagreement_score":0.03871859,"about_ca_system_score_codex":0.00007411974,"about_ca_system_score_gemma":0.00016049061,"threshold_uncertainty_score":0.9989029},"labels":[],"label_agreement":null},{"id":"W2097068816","doi":"10.1142/s1793042109002638","title":"GAUSSIAN LAWS ON DRINFELD MODULES","year":2009,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Automorphism; Finite field; Combinatorics; Conjecture; Ideal (ethics); Polynomial ring; Rank (graph theory); Discrete mathematics; Commutative ring; Polynomial; Commutative property","score_opus":0.009838271542811661,"score_gpt":0.27216425060165284,"score_spread":0.2623259790588412,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2097068816","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.13950357,0.00012852154,0.61090136,0.014479829,0.004944126,0.00009369279,0.000020987116,0.00015651608,0.22977139],"genre_scores_gemma":[0.9903628,0.000015871135,0.0061741914,0.0027300394,0.00044253859,5.494644e-7,0.0000010213262,0.000004429118,0.00026852952],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99888235,0.00012254012,0.00027940792,0.00012303801,0.000465584,0.00012705689],"domain_scores_gemma":[0.99904376,0.00024659315,0.00022072185,0.00020666108,0.00019894238,0.00008329936],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006181498,0.00010163443,0.0001199057,0.00018340611,0.00004630005,0.00014650203,0.0014225091,0.000053412547,0.0005579729],"category_scores_gemma":[0.00009055017,0.00008172264,0.00019530147,0.000120589255,0.000037910053,0.00043999703,0.000056712015,0.00029158656,0.000103020204],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00010280568,0.00012920311,0.0001238948,4.1075546e-7,0.000057108904,0.000110359164,0.00021517069,0.000052463456,0.0001645862,0.8774388,0.0029735388,0.11863167],"study_design_scores_gemma":[0.0003776197,0.00019353336,0.0050102524,0.00008900228,0.000005633897,0.00041928326,0.0000266021,0.00013315491,0.0010197343,0.9651942,0.027415028,0.00011591298],"about_ca_topic_score_codex":4.336784e-7,"about_ca_topic_score_gemma":2.948687e-7,"teacher_disagreement_score":0.8508593,"about_ca_system_score_codex":0.00003464926,"about_ca_system_score_gemma":0.000026832451,"threshold_uncertainty_score":0.6109412},"labels":[],"label_agreement":null},{"id":"W2098995696","doi":"10.1142/s1793042106000383","title":"THIRTY-TWO GOLDBACH VARIATIONS","year":2006,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":35,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Dalhousie University","funders":"","keywords":"Mathematical proof; Variety (cybernetics); Goldbach's conjecture; Euler's formula; Identity (music); Harmonic number; Algebra over a field","score_opus":0.022191505380332214,"score_gpt":0.3536649628456861,"score_spread":0.3314734574653539,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2098995696","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.050073538,0.00012188053,0.52846533,0.0014826357,0.0028162056,0.0001745915,0.00014005961,0.00011598099,0.4166098],"genre_scores_gemma":[0.8553477,0.000013886558,0.110146984,0.00018806366,0.0020384656,0.0000082625775,0.000012851534,0.000051563344,0.032192204],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9983636,0.00010535263,0.0006568513,0.00008875914,0.00064206193,0.00014338005],"domain_scores_gemma":[0.99689835,0.0016924788,0.00054682145,0.00014699249,0.000666036,0.00004929775],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00070069515,0.00012002299,0.00021246524,0.00011788958,0.000044453343,0.000080901234,0.0004967736,0.000044468863,0.005008312],"category_scores_gemma":[0.0011455185,0.000100054545,0.00018240341,0.0000756871,0.000082622006,0.00042427916,0.00007480349,0.0002142167,0.00019090742],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00003345126,0.00026786228,0.00014080074,0.000008484926,0.00013761953,0.00006657866,0.00014815382,0.00003903201,0.00014821625,0.9750224,0.023640811,0.00034662327],"study_design_scores_gemma":[0.0005475137,0.000011999558,0.00021645532,0.00009218734,0.000047070473,0.00054302,0.00012313052,0.00005391194,0.00037214317,0.99118346,0.0067085125,0.00010062503],"about_ca_topic_score_codex":0.000007613254,"about_ca_topic_score_gemma":0.000008322835,"teacher_disagreement_score":0.8052742,"about_ca_system_score_codex":0.00013178613,"about_ca_system_score_gemma":0.000057606558,"threshold_uncertainty_score":0.9959012},"labels":[],"label_agreement":null},{"id":"W2100898148","doi":"10.1142/s1793042109002079","title":"SPECIAL VALUES OF THE POLYGAMMA FUNCTIONS","year":2009,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"Leibniz-Gemeinschaft","keywords":"Mathematics; Dirichlet distribution; Dirichlet series; Analytic number theory; Natural number; Combinatorics; Independence (probability theory); Value (mathematics); Pure mathematics; Discrete mathematics; Mathematical analysis; Statistics","score_opus":0.03690565332791957,"score_gpt":0.36128339468108656,"score_spread":0.324377741353167,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2100898148","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.5149364,0.00007595971,0.01064204,0.0064646173,0.0069135386,0.00025926973,0.00015553733,0.00003381326,0.46051884],"genre_scores_gemma":[0.9733746,0.000011083933,0.0011315995,0.00025537316,0.0057866764,8.425045e-7,0.0000016202027,0.00001677161,0.019421427],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9977921,0.00030695475,0.0006007264,0.000090031506,0.0010567196,0.00015342001],"domain_scores_gemma":[0.99728316,0.0010359559,0.00055737275,0.00024577667,0.0008081157,0.000069593996],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0014255473,0.00011056433,0.00022382385,0.00012094268,0.00005912982,0.000034333312,0.0010216531,0.000057022695,0.008991095],"category_scores_gemma":[0.0016830767,0.000071827635,0.0003689656,0.00015669323,0.0001917841,0.00018101161,0.00008875121,0.00034102995,0.00008034039],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0006638582,0.0005240502,0.0023050578,0.000007109786,0.00061741646,0.000051233907,0.0010146344,0.000014647631,0.00066690467,0.8031395,0.17392556,0.017069986],"study_design_scores_gemma":[0.00051239197,0.000056438916,0.0032838036,0.00011528501,0.00006396482,0.0004822427,0.0005557257,0.00001153852,0.0010088751,0.9808548,0.012978473,0.000076432865],"about_ca_topic_score_codex":0.0000018624654,"about_ca_topic_score_gemma":0.0000019764232,"teacher_disagreement_score":0.45843822,"about_ca_system_score_codex":0.00011336287,"about_ca_system_score_gemma":0.00014796904,"threshold_uncertainty_score":0.9919148},"labels":[],"label_agreement":null},{"id":"W2100933383","doi":"10.1142/s1793042108001304","title":"THETA FUNCTION IDENTITIES AND REPRESENTATIONS BY CERTAIN QUATERNARY QUADRATIC FORMS","year":2008,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":32,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Quaternary; Pure mathematics; Integer (computer science); Theta function; Function (biology); Quadratic equation; Algebra over a field; Geometry; Computer science","score_opus":0.03479522734411008,"score_gpt":0.34425876817767415,"score_spread":0.3094635408335641,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2100933383","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.85520655,0.00040771218,0.10605594,0.0008142951,0.0012224931,0.00020344814,0.00010370063,0.000073443705,0.03591244],"genre_scores_gemma":[0.9674281,0.00025329556,0.0037359078,0.00012914854,0.00025379393,0.000011107302,0.000013230809,0.000033538778,0.02814191],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9984003,0.00011311649,0.000624696,0.00011677197,0.0006102729,0.00013488346],"domain_scores_gemma":[0.9976844,0.001245954,0.00048940984,0.00014358466,0.00036079242,0.000075856165],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00043778916,0.00013676361,0.00023502081,0.00011886247,0.00010434753,0.00007271608,0.00029969943,0.0000504649,0.0016189874],"category_scores_gemma":[0.00094698364,0.000109211025,0.00012889112,0.000054752472,0.00021539259,0.0009308723,0.000085237545,0.00018608948,0.000047934314],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00035347845,0.00039195418,0.003455234,0.0000718691,0.00080758816,0.00025737716,0.0037516358,0.000014609952,0.0011385375,0.9164761,0.07262486,0.0006567971],"study_design_scores_gemma":[0.00049447257,0.00004570937,0.0003869453,0.00009830338,0.000055944678,0.0019031981,0.0017092032,0.00005484368,0.00049023464,0.9938726,0.00077420654,0.00011435725],"about_ca_topic_score_codex":0.0000068817594,"about_ca_topic_score_gemma":0.000003520305,"teacher_disagreement_score":0.11222153,"about_ca_system_score_codex":0.000070209404,"about_ca_system_score_gemma":0.000035954232,"threshold_uncertainty_score":0.9992937},"labels":[],"label_agreement":null},{"id":"W2101885939","doi":"10.1142/s1793042115500311","title":"Sums of digits in q-ary expansions","year":2014,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Base (topology); Rational number; Expression (computer science); Of the form; Multiple","score_opus":0.04164528069980739,"score_gpt":0.3798568663269006,"score_spread":0.3382115856270932,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2101885939","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9073985,0.000039625244,0.01423281,0.0006877769,0.0006548031,0.00010068258,0.000041603795,0.000015115468,0.07682906],"genre_scores_gemma":[0.9955686,0.000017325368,0.0021829417,0.000114023744,0.000266124,0.0000020904772,0.0000032418645,0.00002303217,0.0018226206],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99770504,0.00039632132,0.00077615294,0.00010711206,0.0008387962,0.00017657597],"domain_scores_gemma":[0.99540436,0.00318451,0.00046907627,0.00020646925,0.00061746314,0.00011812334],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0026047882,0.00011386288,0.00032018812,0.00027660272,0.000016881173,0.000023820825,0.0007733407,0.00006621191,0.0041480083],"category_scores_gemma":[0.004508175,0.00009311562,0.00018948404,0.00014433006,0.0001465987,0.00024247244,0.000130388,0.0003250775,0.00006608438],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00056719605,0.0004914619,0.014733167,0.000034634973,0.00037703742,0.00013379905,0.0011596879,0.000028215973,0.0012370126,0.9617094,0.008570566,0.010957846],"study_design_scores_gemma":[0.0009247836,0.00004922512,0.0015968082,0.00032236782,0.00002078263,0.00028033688,0.00043697862,0.0001209975,0.0015657095,0.99112475,0.003457064,0.00010021279],"about_ca_topic_score_codex":0.0000074856216,"about_ca_topic_score_gemma":0.000009050006,"teacher_disagreement_score":0.08817008,"about_ca_system_score_codex":0.000093283925,"about_ca_system_score_gemma":0.00012334119,"threshold_uncertainty_score":0.99676234},"labels":[],"label_agreement":null},{"id":"W2102578010","doi":"10.1142/s1793042113500267","title":"A SOLUTION OF SUN'S $520 CHALLENGE CONCERNING $\\frac{520}{\\pi}$","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Legendre polynomials; Modular form; Hypergeometric function; Series (stratigraphy); Representation (politics); Algebra over a field; Generating function; Function (biology)","score_opus":0.050351789427697795,"score_gpt":0.35283407981724046,"score_spread":0.30248229038954266,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2102578010","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.60904473,0.00076355826,0.23943472,0.0033042987,0.0032796534,0.0005945253,0.00011032468,0.00013005453,0.14333816],"genre_scores_gemma":[0.9710096,0.00007954177,0.0247197,0.00007373127,0.0004950453,0.000011096132,0.0000033954432,0.00003540915,0.003572492],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99799377,0.00013315179,0.0008447932,0.000108018256,0.0007414572,0.00017881638],"domain_scores_gemma":[0.9960298,0.0016509625,0.00095959654,0.00016293497,0.0011121355,0.00008460046],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0006866065,0.0001486671,0.0003512314,0.0001283148,0.00003460508,0.000048151425,0.00053851015,0.00007811494,0.00884259],"category_scores_gemma":[0.0019562282,0.00012548636,0.00022027253,0.000054646418,0.000178275,0.00067582366,0.00012768664,0.0002746205,0.00020679462],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00012034819,0.00044815944,0.00024558514,0.00012435201,0.00058026286,0.000056256926,0.0025934712,0.000030839365,0.0016869389,0.97732127,0.011625157,0.0051673865],"study_design_scores_gemma":[0.0005533007,0.000054644308,0.000114157745,0.0004397198,0.000044000946,0.00022902644,0.0010220611,0.00019490447,0.0011019249,0.99459195,0.0015332815,0.00012102164],"about_ca_topic_score_codex":0.000011421787,"about_ca_topic_score_gemma":0.000002955615,"teacher_disagreement_score":0.36196488,"about_ca_system_score_codex":0.00012753277,"about_ca_system_score_gemma":0.000056874254,"threshold_uncertainty_score":0.99206346},"labels":[],"label_agreement":null},{"id":"W2102816632","doi":"10.1142/s1793042112500108","title":"ASYMPTOTICS OF THE WEIGHTED DELANNOY NUMBERS","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada; Killam Trusts","keywords":"Mathematics; Divisibility rule; Diagonal; Asymptotic formula; Generalization; Asymptotic expansion; Combinatorics; Pure mathematics; Mathematical analysis; Geometry","score_opus":0.04288284500885192,"score_gpt":0.3162240830437284,"score_spread":0.2733412380348765,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2102816632","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.79129666,0.00006858434,0.056799583,0.0003364384,0.011151326,0.0003190145,0.00009776144,0.000053685653,0.13987695],"genre_scores_gemma":[0.9583602,0.000011736537,0.040460743,0.00008850715,0.00029526546,0.0000019799188,7.912154e-7,0.000034181652,0.00074657367],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.998114,0.00016355886,0.0007772555,0.000079866004,0.00073162274,0.00013372522],"domain_scores_gemma":[0.9965487,0.00095525116,0.0012233587,0.0002819152,0.00093178713,0.000059002392],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00067803165,0.00013750332,0.00026616812,0.00007054473,0.000031356165,0.000012192418,0.0011339373,0.00007668658,0.0017474422],"category_scores_gemma":[0.0013545435,0.00009124759,0.000262073,0.00012238091,0.00014752884,0.00018590703,0.00015453604,0.0002775921,0.00002642663],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00017269357,0.00035029315,0.0015723234,0.000018157987,0.00041567007,0.00002873233,0.0021426296,0.0000017253809,0.00013579699,0.9913778,0.0029934065,0.0007907721],"study_design_scores_gemma":[0.0005778377,0.00003442626,0.00038908198,0.00020464968,0.0000731534,0.00036197843,0.00036843997,0.000015938516,0.0053994134,0.9910144,0.0014665155,0.00009412496],"about_ca_topic_score_codex":0.000002271238,"about_ca_topic_score_gemma":0.0000014092969,"teacher_disagreement_score":0.16706356,"about_ca_system_score_codex":0.000093724026,"about_ca_system_score_gemma":0.00009085035,"threshold_uncertainty_score":0.9991651},"labels":[],"label_agreement":null},{"id":"W2104946632","doi":"10.1142/s1793042105000054","title":"ON SUMS OF THREE SQUARES","year":2005,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Mathematics; Integer (computer science); Mathematical proof; Conjecture; Combinatorics; Asymptotic formula; Residual sum of squares; Value (mathematics); Explained sum of squares; Square (algebra); Lack-of-fit sum of squares; Multiple; Discrete mathematics; Statistics; Arithmetic; Non-linear least squares","score_opus":0.05169747263344705,"score_gpt":0.3848388555107305,"score_spread":0.33314138287728345,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2104946632","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.87854904,0.00007841654,0.019715691,0.0017636884,0.00069288356,0.0001282085,0.00008578419,0.000025085788,0.098961174],"genre_scores_gemma":[0.9928204,0.00001232446,0.0038761054,0.00017516848,0.00065009773,0.0000017526045,0.0000022594832,0.000027086428,0.0024348414],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99769956,0.00018357743,0.0006746856,0.000105989224,0.0011663247,0.00016987098],"domain_scores_gemma":[0.99545556,0.0028601675,0.0005546075,0.00022234175,0.00081422465,0.000093110284],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001797286,0.00012835514,0.00027980286,0.0002073157,0.00002521863,0.000028240667,0.00087292,0.00006416049,0.014081744],"category_scores_gemma":[0.0018617519,0.00009962252,0.00026329292,0.00008927809,0.00015605884,0.00020382811,0.00009074447,0.00032667918,0.00025813084],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00087936694,0.00035051373,0.0014211256,0.000013387122,0.00058156037,0.00006899712,0.00037441228,0.00004687011,0.00031044308,0.96232766,0.020323794,0.013301853],"study_design_scores_gemma":[0.0008065498,0.000094415635,0.00037742377,0.00020295953,0.000036340298,0.00027585903,0.00017501852,0.00010186611,0.0029142012,0.9899912,0.004926077,0.000098078635],"about_ca_topic_score_codex":0.000003447297,"about_ca_topic_score_gemma":0.00001162628,"teacher_disagreement_score":0.1142713,"about_ca_system_score_codex":0.0001418798,"about_ca_system_score_gemma":0.00009674449,"threshold_uncertainty_score":0.9868195},"labels":[],"label_agreement":null},{"id":"W2107619650","doi":"10.1142/s1793042106000504","title":"TRIANGLE-RECTANGLE PAIRS WITH A COMMON AREA AND A COMMON PERIMETER","year":2006,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Mathematics and Applications","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Isosceles triangle; Rectangle; Perimeter; Mathematics; Combinatorics; Geometry","score_opus":0.025282484975883705,"score_gpt":0.310011134617336,"score_spread":0.2847286496414523,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2107619650","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.94726914,0.00007928969,0.008420092,0.0008654129,0.00012175994,0.00015003525,0.00007136624,0.00002643133,0.042996492],"genre_scores_gemma":[0.98026496,0.000005395311,0.018223139,0.00009307062,0.0001715419,0.000010807214,0.000007909442,0.000022479531,0.0012006696],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9989648,0.000072887815,0.0004315477,0.00008467917,0.00034647013,0.00009961337],"domain_scores_gemma":[0.99824595,0.0009143336,0.00043762662,0.00013413046,0.00021698452,0.00005094987],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005108643,0.00011561831,0.00025501853,0.00007969913,0.00004599757,0.00007456839,0.0002522368,0.000040811217,0.00091880764],"category_scores_gemma":[0.00008350116,0.00008126199,0.00009571093,0.000059018188,0.000077655575,0.000106705425,0.00004118435,0.00014606354,0.0000106682255],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00086721417,0.0017786915,0.01271616,0.00007026696,0.00085088686,0.0002636145,0.0016524645,0.000018038694,0.001370588,0.85569596,0.11671416,0.008001975],"study_design_scores_gemma":[0.001478395,0.000103195605,0.0010611094,0.00027076542,0.000104413026,0.0017105113,0.00036671446,0.00020236672,0.00092791877,0.97323203,0.020354243,0.00018831971],"about_ca_topic_score_codex":0.000015759098,"about_ca_topic_score_gemma":0.000042941865,"teacher_disagreement_score":0.117536105,"about_ca_system_score_codex":0.000042450887,"about_ca_system_score_gemma":0.000026551319,"threshold_uncertainty_score":0.9999945},"labels":[],"label_agreement":null},{"id":"W2111378006","doi":"10.1142/s1793042114500377","title":"Computations with Witt vectors and the Greenberg transform","year":2014,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":false,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"","funders":"Centre de Recherches Mathématiques","keywords":"Witt vector; Computation; Mathematics; Polynomial; Algebra over a field; Pure mathematics; Algorithm; Mathematical analysis","score_opus":0.010708349796614424,"score_gpt":0.2894111766300658,"score_spread":0.2787028268334514,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2111378006","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.116079666,0.00001975267,0.87571263,0.0011612426,0.00028186638,0.00009115116,0.000013905017,0.000011642379,0.006628125],"genre_scores_gemma":[0.9939579,0.000007242896,0.0053757858,0.000104502564,0.00022455407,0.0000039919805,0.0000033253557,0.000010892449,0.00031182394],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9990766,0.00014709323,0.0003140676,0.000059755053,0.00033169345,0.00007079106],"domain_scores_gemma":[0.9975412,0.0018073318,0.0002603834,0.00006871599,0.00027539593,0.00004697138],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005437097,0.00007915935,0.00016609022,0.000041942953,0.000060909624,0.000046153298,0.0001907442,0.000024676141,0.00021394454],"category_scores_gemma":[0.0002650974,0.00004089946,0.00007356763,0.000046962246,0.0001652864,0.00012955061,0.000015791322,0.00012785105,0.0000054922907],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00036193905,0.000051538565,0.00025625533,0.0000062942063,0.00019762307,0.000003412191,0.00056544907,0.00014221326,0.000007687307,0.98560756,0.00014731823,0.012652707],"study_design_scores_gemma":[0.002088339,0.000045431672,0.0006055037,0.00009646476,0.000056441284,0.00030546953,0.00020944452,0.0028254965,0.000012168414,0.99141085,0.0022759552,0.000068451445],"about_ca_topic_score_codex":0.000007556604,"about_ca_topic_score_gemma":0.000020643633,"teacher_disagreement_score":0.8778782,"about_ca_system_score_codex":0.000026385846,"about_ca_system_score_gemma":0.00001755326,"threshold_uncertainty_score":0.23425429},"labels":[],"label_agreement":null},{"id":"W2111512361","doi":"10.1142/s179304211000323x","title":"SMALL VALUE ESTIMATES FOR THE ADDITIVE GROUP","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Functional Equations Stability Results","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Ottawa","funders":"","keywords":"Mathematics; Extension (predicate logic); Combinatorics; Group (periodic table); Sequence (biology); Context (archaeology); Fixed point; Discrete mathematics; Pure mathematics; Mathematical analysis","score_opus":0.043030381714338366,"score_gpt":0.3363595301644256,"score_spread":0.29332914845008723,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2111512361","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.26189375,0.00013206762,0.6805924,0.011715683,0.018187884,0.0011609229,0.0023152065,0.00011730833,0.023884764],"genre_scores_gemma":[0.8760728,0.00000995055,0.11968943,0.0004977811,0.0024826045,0.00006310724,0.00005050004,0.000044157263,0.0010896599],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9987964,0.00006902464,0.00046937086,0.000106109044,0.00043706447,0.00012203645],"domain_scores_gemma":[0.98166215,0.016521823,0.0004272192,0.0001727672,0.0011633119,0.00005273731],"candidate_categories":["metaresearch","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0016314029,0.000113698836,0.00014781741,0.00006653378,0.0000979734,0.00007170441,0.00061804923,0.00006418056,0.0024148559],"category_scores_gemma":[0.011181913,0.00007405106,0.0002362126,0.0000568124,0.00015340622,0.00017697991,0.000057045283,0.0003521506,0.000041601485],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00058442407,0.00023971694,0.00023672581,0.000007452058,0.0005228832,0.0000070066108,0.00037845774,0.000042887827,0.0008183228,0.9764892,0.01092366,0.009749251],"study_design_scores_gemma":[0.00074209314,0.0000512282,0.001288195,0.000039512986,0.00008935703,0.00034959358,0.00024322489,0.0008500626,0.0006726257,0.9677958,0.02779033,0.00008800318],"about_ca_topic_score_codex":0.0000055057567,"about_ca_topic_score_gemma":0.00003086078,"teacher_disagreement_score":0.6141791,"about_ca_system_score_codex":0.00006457374,"about_ca_system_score_gemma":0.0000951722,"threshold_uncertainty_score":0.99849707},"labels":[],"label_agreement":null},{"id":"W2114968535","doi":"10.1142/s1793042105000352","title":"ON AN ELEMENTARY APPROACH TO THE LEBESGUE–NAGELL EQUATION","year":2005,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Diophantine equation; Lebesgue integration; Elementary theory; Pure mathematics; Integer (computer science)","score_opus":0.016803880405761508,"score_gpt":0.31612633097662174,"score_spread":0.2993224505708602,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2114968535","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.034199566,0.000006846522,0.8639088,0.0026222114,0.00019421654,0.00014018983,0.00010487805,0.000008985107,0.0988143],"genre_scores_gemma":[0.9757937,0.0000011159551,0.020219749,0.0013649294,0.0018409113,0.000016430467,0.000041476877,0.000011448129,0.0007102249],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9992199,0.000058816087,0.00026434794,0.000086149674,0.00027825453,0.0000925121],"domain_scores_gemma":[0.99915814,0.00031682805,0.0001657562,0.00014141147,0.00015063354,0.000067236164],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0004043563,0.00007923971,0.00008420588,0.000024672014,0.00006457372,0.000047368805,0.00045221188,0.000011543002,0.002808526],"category_scores_gemma":[0.000029196042,0.00005167269,0.000081431506,0.000052641873,0.000027139442,0.00020015614,0.00003950345,0.00013540163,0.00022264353],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000058546222,0.00032457625,0.000052310825,4.4541414e-7,0.00006900934,2.4131552e-7,0.00032473347,0.003022751,0.00005164986,0.9368407,0.0051408797,0.05411416],"study_design_scores_gemma":[0.000305403,0.000038871545,0.000089410576,0.000022255655,0.000017078573,0.0000086624495,0.0009742886,0.00056817697,0.00048212896,0.8930721,0.10433606,0.00008555611],"about_ca_topic_score_codex":0.0000023752566,"about_ca_topic_score_gemma":3.630947e-7,"teacher_disagreement_score":0.9415941,"about_ca_system_score_codex":0.00003714331,"about_ca_system_score_gemma":0.000017065715,"threshold_uncertainty_score":0.998103},"labels":[],"label_agreement":null},{"id":"W2117095608","doi":"10.1142/s1793042108001614","title":"BERNDT'S CURIOUS FORMULA","year":2008,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Ramanujan's sum; Integer (computer science); Pure mathematics; Arithmetic function; Arithmetic; Combinatorics; Discrete mathematics","score_opus":0.05076704654807616,"score_gpt":0.3694805102014368,"score_spread":0.3187134636533606,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2117095608","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.6661847,0.00026746767,0.14746232,0.001204651,0.0035038851,0.00022736282,0.000099064084,0.00013806392,0.18091244],"genre_scores_gemma":[0.9327036,0.00012898828,0.046453267,0.00030443282,0.0010156654,0.0000053416547,0.0000037429795,0.000051054,0.019333888],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99841326,0.00006345163,0.0005800435,0.00008192356,0.0007128922,0.0001484248],"domain_scores_gemma":[0.99748814,0.0012369702,0.00047676716,0.00014310698,0.00057166297,0.00008333497],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.000419564,0.00012192809,0.00024259233,0.000102668346,0.000053781747,0.000029274683,0.0005542785,0.00005082596,0.00412123],"category_scores_gemma":[0.0017193236,0.0000990866,0.00021165195,0.000051320563,0.00013887577,0.00047269557,0.00009275698,0.00022316148,0.0001997707],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00014513708,0.00031065798,0.00034142082,0.000021143262,0.00035409894,0.0008061237,0.0014787174,0.000008375788,0.00016875245,0.9581398,0.037023377,0.0012024197],"study_design_scores_gemma":[0.00048683718,0.000024276607,0.00013132392,0.00010400057,0.000025311281,0.004509873,0.00017644014,0.000011773784,0.00070483686,0.9837207,0.010001299,0.00010332012],"about_ca_topic_score_codex":0.0000011701414,"about_ca_topic_score_gemma":0.0000011351326,"teacher_disagreement_score":0.26651886,"about_ca_system_score_codex":0.00010696683,"about_ca_system_score_gemma":0.00006070705,"threshold_uncertainty_score":0.99678916},"labels":[],"label_agreement":null},{"id":"W2120535745","doi":"10.1142/s1793042116500019","title":"Evaluation of the convolution sums ∑l+27m=nσ(l)σ(m) and ∑l+32m=nσ(l)σ(m)","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Convolution (computer science); Combinatorics; Quadratic equation; Pure mathematics; Geometry; Artificial intelligence; Computer science","score_opus":0.14820776021076512,"score_gpt":0.4187511864288494,"score_spread":0.27054342621808425,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2120535745","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.940979,0.00071260874,0.017501002,0.0010470963,0.0028870164,0.00038392117,0.00006847308,0.000027484699,0.03639341],"genre_scores_gemma":[0.99452007,0.000023575378,0.0037777172,0.000059070753,0.00028104137,0.000005790752,0.0000017565626,0.000019559715,0.0013114449],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99678683,0.0004581269,0.00064311037,0.00009506902,0.0019040821,0.00011279057],"domain_scores_gemma":[0.99503064,0.0009284852,0.000826775,0.00018552828,0.0029483926,0.000080202495],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0045994553,0.000118587894,0.0002368755,0.000083500345,0.000032951444,0.000037492195,0.00043389376,0.00006337217,0.0006316999],"category_scores_gemma":[0.0072627524,0.000081305945,0.00013011442,0.000080478465,0.00024181399,0.00038830476,0.00011045661,0.00019014558,0.000017644219],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00024613712,0.00038031337,0.0017055881,0.00005708738,0.00068999076,0.000011823025,0.0030685717,0.00015812092,0.0011429633,0.97153026,0.015110778,0.0058983895],"study_design_scores_gemma":[0.0010920514,0.000030187502,0.00071844005,0.00023786796,0.00022452459,0.00031117038,0.0011036461,0.000411926,0.0018722638,0.99311435,0.0008010181,0.00008255362],"about_ca_topic_score_codex":0.00000455533,"about_ca_topic_score_gemma":0.000007868656,"teacher_disagreement_score":0.053541057,"about_ca_system_score_codex":0.00023825666,"about_ca_system_score_gemma":0.00021722054,"threshold_uncertainty_score":0.8694717},"labels":[],"label_agreement":null},{"id":"W2125748030","doi":"10.1142/s1793042112500595","title":"FOURIER SERIES OF A CLASS OF ETA QUOTIENTS","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":30,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Quotient; Dedekind eta function; Fourier series; Class (philosophy); Dedekind cut; Pure mathematics; Dedekind sum; Combinatorics; Function (biology); Series (stratigraphy); Modular form; Eisenstein series; Mathematical analysis","score_opus":0.027587322065793826,"score_gpt":0.3204467590113193,"score_spread":0.29285943694552546,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2125748030","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9886928,0.00011850743,0.0010490529,0.00011485879,0.003167866,0.000043290205,0.000029777442,0.0000043830314,0.00677943],"genre_scores_gemma":[0.9965108,0.000011876735,0.0024441076,0.000037877548,0.0005202322,8.3556984e-7,0.0000012739023,0.000013261743,0.00045972923],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.998622,0.00009053375,0.0005422876,0.000045138662,0.0005900943,0.0001099377],"domain_scores_gemma":[0.99811316,0.0003675461,0.0007751963,0.00012046534,0.0005640738,0.00005955654],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00047336958,0.00008796128,0.00024057733,0.00007049802,0.000012539867,0.000007952762,0.00037679877,0.000059744056,0.0015860213],"category_scores_gemma":[0.00047222432,0.00006783404,0.00018278493,0.000046134777,0.00008446219,0.0002959216,0.00007571501,0.000128738,0.0000042957677],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00034587286,0.00017311175,0.004200668,0.000017738179,0.00039844506,0.0000034324885,0.0012453125,0.0000030573804,0.00018171969,0.9908352,0.0015991073,0.0009963287],"study_design_scores_gemma":[0.00053347426,0.000051020346,0.0011290195,0.00010677535,0.00005002067,0.00017225876,0.00035355517,0.000003210239,0.0033379826,0.9913888,0.00280992,0.000063944266],"about_ca_topic_score_codex":0.000002634062,"about_ca_topic_score_gemma":3.9248573e-7,"teacher_disagreement_score":0.0078179715,"about_ca_system_score_codex":0.00003644092,"about_ca_system_score_gemma":0.00004707262,"threshold_uncertainty_score":0.99932665},"labels":[],"label_agreement":null},{"id":"W2127097035","doi":"10.1142/s1793042114500353","title":"On the number of representations of a positive integer as a sum of two binary quadratic forms","year":2014,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"York University; Carleton University","funders":"","keywords":"Combinatorics; Mathematics; Integer (computer science); Binary quadratic form; Isotropic quadratic form; Quadratic equation; Binary number; Quadratic form (statistics); Discrete mathematics; Quadratic function; Arithmetic","score_opus":0.03283142181660513,"score_gpt":0.4036920663441857,"score_spread":0.37086064452758055,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2127097035","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.90326786,0.000010199966,0.011133108,0.0009172654,0.00021916532,0.00018345017,0.0000842638,0.000006403185,0.084178284],"genre_scores_gemma":[0.9964747,0.000008147897,0.0013154885,0.00013477792,0.00011675598,0.0000067664264,0.0000058303785,0.0000293218,0.0019082149],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9964994,0.0007653415,0.0011436451,0.00013952935,0.0012773748,0.00017471219],"domain_scores_gemma":[0.98641485,0.009979152,0.001420258,0.00039218148,0.0017158348,0.00007774346],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0031334406,0.00016576843,0.00046743115,0.00020986893,0.000039525323,0.000019975505,0.0009548538,0.000063876825,0.006590485],"category_scores_gemma":[0.0052023204,0.000105826504,0.0004113249,0.00021945055,0.00048129613,0.0002164544,0.00016661796,0.00039024447,0.00007982148],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0009690235,0.00060755195,0.0026352666,0.000038772247,0.0009791141,0.000021733624,0.0020080316,0.00004402277,0.0015256669,0.98855054,0.0021839768,0.0004362965],"study_design_scores_gemma":[0.0009715678,0.00017646723,0.0006125253,0.0006360135,0.00010662744,0.00033484443,0.001983384,0.0003217045,0.00941862,0.98528755,0.00005585639,0.00009485666],"about_ca_topic_score_codex":0.000047997517,"about_ca_topic_score_gemma":0.0000064439755,"teacher_disagreement_score":0.09320683,"about_ca_system_score_codex":0.00008781914,"about_ca_system_score_gemma":0.00016668804,"threshold_uncertainty_score":0.99431765},"labels":[],"label_agreement":null},{"id":"W2128455495","doi":"10.1142/s1793042110002971","title":"THE DIOPHANTINE EQUATION A<sup>4</sup> + 2<sup>δ</sup>B<sup>2</sup> = C<sup>n</sup>","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":43,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Lethbridge; University of British Columbia","funders":"","keywords":"Mathematics; Diophantine equation; Prime (order theory); Combinatorics; Physics","score_opus":0.02104715907661403,"score_gpt":0.2953143442989366,"score_spread":0.2742671852223226,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2128455495","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9575598,0.00047406435,0.011826241,0.0041022063,0.002178989,0.00080614054,0.00041494856,0.0002617341,0.022375846],"genre_scores_gemma":[0.97466195,0.00027134665,0.0034752816,0.0013913134,0.006480199,0.000069786285,0.0001761743,0.00029803856,0.013175939],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9890541,0.0016391852,0.003282974,0.0010120706,0.0035510377,0.0014606349],"domain_scores_gemma":[0.9846377,0.0084972,0.002226081,0.0015229102,0.0023875693,0.0007285575],"candidate_categories":["metaepi_narrow","research_integrity","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.008780924,0.0012600461,0.0014148107,0.00082094467,0.0009572616,0.0008080467,0.003892841,0.0008368528,0.015077317],"category_scores_gemma":[0.007406186,0.0009951385,0.00139254,0.00081204006,0.00094632985,0.0018794205,0.0008214915,0.0033665213,0.0021522953],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0055156252,0.0035840636,0.0053417683,0.0003341561,0.0068110367,0.0012201234,0.02768658,0.022022912,0.0013027948,0.82176095,0.06587681,0.038543154],"study_design_scores_gemma":[0.0059640156,0.0003876733,0.00048563172,0.00089119707,0.00073536084,0.004616455,0.010268731,0.03724386,0.0021996913,0.85147834,0.0840588,0.00167023],"about_ca_topic_score_codex":0.000044011238,"about_ca_topic_score_gemma":0.00001037112,"teacher_disagreement_score":0.036872923,"about_ca_system_score_codex":0.00045047654,"about_ca_system_score_gemma":0.0005351608,"threshold_uncertainty_score":0.9992499},"labels":[],"label_agreement":null},{"id":"W2129474691","doi":"10.1142/s179304210800133x","title":"BALANCED SETS AND THE VECTOR GAME","year":2008,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Computability, Logic, AI Algorithms","field":"Computer Science","cited_by":10,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Modulo; Mathematics; Combinatorics; Cardinality (data modeling); Prime (order theory); Upper and lower bounds; Context (archaeology); Discrete mathematics; Factorization; Prime factor; Algorithm","score_opus":0.012523262202644094,"score_gpt":0.2620415997820041,"score_spread":0.24951833757935998,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2129474691","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.43383682,0.00064695213,0.5387368,0.013274386,0.005396283,0.00019402924,0.000021765296,0.00008092339,0.0078120446],"genre_scores_gemma":[0.98790765,0.00007118277,0.010572256,0.00085325824,0.00038853346,0.0000022164031,6.580303e-7,0.000005744572,0.00019849703],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.998559,0.0002668411,0.00034178674,0.00014394896,0.00056218513,0.00012621612],"domain_scores_gemma":[0.9979069,0.001120989,0.0002672999,0.00020984707,0.0004234901,0.00007143421],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00095488306,0.00010120449,0.00017938232,0.000060852308,0.00005905699,0.00009578336,0.0013602403,0.000032313972,0.00026000466],"category_scores_gemma":[0.00035903353,0.000063628126,0.0001254894,0.00009558907,0.00028057763,0.00037657036,0.0003157145,0.00022049602,0.00003703197],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0009518764,0.00045633942,0.012024361,0.000009662338,0.0007742058,0.0013282418,0.010646153,0.00047230293,0.00022348965,0.79614943,0.012266592,0.16469735],"study_design_scores_gemma":[0.005423599,0.0001193632,0.105061516,0.00007566606,0.000021075966,0.020142695,0.00010036759,0.021406993,0.00028703912,0.8269638,0.020066187,0.00033170125],"about_ca_topic_score_codex":0.000005554413,"about_ca_topic_score_gemma":8.721843e-7,"teacher_disagreement_score":0.55407083,"about_ca_system_score_codex":0.00006161446,"about_ca_system_score_gemma":0.00008444484,"threshold_uncertainty_score":0.28468686},"labels":[],"label_agreement":null},{"id":"W2129660780","doi":"10.1142/s179304211000371x","title":"RAMANUJAN CONGRUENCES FOR SIEGEL MODULAR FORMS","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Ramanujan's sum; Congruence relation; Mathematics; Siegel modular form; Modular form; Pure mathematics; Modular design; Ramanujan theta function; Type (biology); Algebra over a field; Computer science","score_opus":0.018161674929133214,"score_gpt":0.3594280317754529,"score_spread":0.3412663568463197,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2129660780","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9211943,0.000023912115,0.07051976,0.0005622185,0.0024720568,0.0001050322,0.000081323706,0.000018850293,0.005022554],"genre_scores_gemma":[0.9727301,0.000007614136,0.024646208,0.00025767577,0.0009321183,0.000006508958,0.0000070527967,0.000020099176,0.0013926483],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9989447,0.000023595368,0.00041295227,0.00009203806,0.0003829284,0.00014381028],"domain_scores_gemma":[0.99751544,0.0012167561,0.00042936395,0.000120566096,0.00063970784,0.00007814341],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007348993,0.00010687827,0.00018484528,0.000104558785,0.000044221477,0.000047857433,0.0005371469,0.00007039693,0.0029284784],"category_scores_gemma":[0.0016772624,0.00007894924,0.00020535334,0.000049885602,0.00008537705,0.00035808334,0.000041133422,0.00027437642,0.00004272018],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00024391428,0.00015606175,0.00076189754,0.000014086738,0.00028669802,0.000035962672,0.00024676142,0.00001163012,0.003554959,0.97514,0.0046932483,0.014854792],"study_design_scores_gemma":[0.00068807177,0.000039669056,0.00028088657,0.000038326678,0.000024416464,0.00037460722,0.00022737127,0.00004243247,0.0037737503,0.9752996,0.019111266,0.00009959313],"about_ca_topic_score_codex":2.6647012e-7,"about_ca_topic_score_gemma":0.000005406976,"teacher_disagreement_score":0.051535785,"about_ca_system_score_codex":0.00002528017,"about_ca_system_score_gemma":0.00004929263,"threshold_uncertainty_score":0.997983},"labels":[],"label_agreement":null},{"id":"W2134760766","doi":"10.1142/s1793042111004162","title":"ON THE NUMBER OF RATIONAL ITERATED PREIMAGES OF THE ORIGIN UNDER QUADRATIC DYNAMICAL SYSTEMS","year":2011,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"McGill University","funders":"","keywords":"Mathematics; Iterated function; Rational number; Conjecture; Quadratic equation; Bounded function; Rational point; Endomorphism; Affine transformation; Rational function; Bounding overwatch; Discrete mathematics; Pure mathematics; Combinatorics; Geometry; Computer science; Algebraic number; Mathematical analysis","score_opus":0.04498382754537024,"score_gpt":0.3322322938575922,"score_spread":0.28724846631222195,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2134760766","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.95515674,0.00010629848,0.010266114,0.00096239184,0.0056535164,0.0005079499,0.0004504358,0.000021909113,0.026874654],"genre_scores_gemma":[0.9960067,0.000017028355,0.0006579628,0.00019376392,0.00047409258,0.000019884177,0.00002286467,0.00005051437,0.002557158],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9948049,0.0015531714,0.0016799846,0.00024582015,0.0015130196,0.00020308026],"domain_scores_gemma":[0.9888293,0.0057450603,0.0030998923,0.00065571594,0.0015977089,0.000072299976],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002869472,0.00037633162,0.0007062628,0.00015193746,0.00007290532,0.0000794325,0.0021324237,0.00031082585,0.006989468],"category_scores_gemma":[0.0019753543,0.00021115203,0.0006775101,0.0001710088,0.00050447136,0.00015003394,0.00050909,0.0012558545,0.000060052775],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0006514661,0.00056566973,0.001083083,0.00016472342,0.0019660904,0.000012955998,0.0009156753,0.00061156834,0.00017474318,0.98863316,0.005152577,0.00006830874],"study_design_scores_gemma":[0.00051802833,0.00003302407,0.00091897557,0.0018306852,0.00023066755,0.00044453543,0.000513824,0.00019767294,0.0014300639,0.99354506,0.00013197248,0.00020550888],"about_ca_topic_score_codex":0.000019380335,"about_ca_topic_score_gemma":0.0000020531943,"teacher_disagreement_score":0.040850002,"about_ca_system_score_codex":0.00018495972,"about_ca_system_score_gemma":0.00043658074,"threshold_uncertainty_score":0.9939183},"labels":[],"label_agreement":null},{"id":"W2135722577","doi":"10.1142/s1793042111004769","title":"ALGEBRAIC INDEPENDENCE OF VALUES OF MODULAR FORMS","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":15,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Modular form; Eisenstein series; Algebraic number; Fourier series; Pure mathematics; Modular design; Hecke operator; Algebra over a field; Singular point of an algebraic variety; Modular curve; Independence (probability theory); Dedekind eta function; Modular elliptic curve; Mathematical analysis; Elliptic curve; Statistics; Computer science","score_opus":0.03827716132830453,"score_gpt":0.32845527284140996,"score_spread":0.2901781115131054,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2135722577","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9533288,0.000088452645,0.035577122,0.000021986425,0.0004128541,0.000043040694,0.000032794935,0.000006944959,0.01048799],"genre_scores_gemma":[0.9873599,0.000027737564,0.01216307,0.000037821184,0.000101486505,8.4910903e-7,0.0000013336773,0.0000143369525,0.0002934678],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9984391,0.000060466562,0.000657582,0.00007594181,0.0006652807,0.00010167817],"domain_scores_gemma":[0.9976164,0.00044934018,0.00094615156,0.00015144137,0.00078696804,0.000049679275],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00075269566,0.00009848579,0.00026319656,0.0001714666,0.000012396946,0.0000046357623,0.00058698026,0.000066203356,0.0027664488],"category_scores_gemma":[0.0008056947,0.00007527786,0.00019708622,0.000093049275,0.00011997007,0.0003340629,0.000081911596,0.00018563245,0.000012604261],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00040977946,0.00044537216,0.005555409,0.00004654701,0.0005752905,0.00006104932,0.0021677911,0.000012229421,0.0022850318,0.9807623,0.0003248946,0.0073542986],"study_design_scores_gemma":[0.00040985693,0.00007342465,0.0029332242,0.000175853,0.00003340289,0.00021982253,0.0004817401,0.000008957795,0.034594376,0.9609369,0.00006159836,0.00007085299],"about_ca_topic_score_codex":0.0000016879101,"about_ca_topic_score_gemma":7.5893837e-7,"teacher_disagreement_score":0.034031082,"about_ca_system_score_codex":0.000028723385,"about_ca_system_score_gemma":0.00005224183,"threshold_uncertainty_score":0.99814516},"labels":[],"label_agreement":null},{"id":"W2143833056","doi":"10.1142/s1793042114500067","title":"Sign changes of Fourier coefficients of half-integral weight cusp forms","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":22,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Cusp (singularity); Sign (mathematics); Cusp form; Fourier series; Fourier analysis; Fourier transform; Mathematical analysis; Space (punctuation); Geometry","score_opus":0.01724733829035756,"score_gpt":0.3096834865535986,"score_spread":0.29243614826324105,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2143833056","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9237485,0.00010879743,0.062405407,0.00059969403,0.0010867221,0.00015442506,0.00009399913,0.0000128950605,0.011789573],"genre_scores_gemma":[0.99109316,0.000026412597,0.006988767,0.000102770646,0.00025690207,0.0000037862146,0.000004809308,0.000020962969,0.0015024176],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9983908,0.000066136985,0.000612878,0.000088187146,0.0006909503,0.00015107424],"domain_scores_gemma":[0.99700356,0.00076434365,0.00092271494,0.00014869108,0.0010870943,0.0000736084],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0004906066,0.00013211787,0.0003220694,0.0002131953,0.00001861782,0.000014899149,0.000528814,0.00006871579,0.0062995264],"category_scores_gemma":[0.00066411064,0.000092066235,0.00020041116,0.0001150828,0.00012598236,0.00026887775,0.00007781047,0.00019035523,0.000051442916],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00057815947,0.0013084073,0.0049270876,0.000118858086,0.0013823292,0.000057181853,0.00198211,0.000058052912,0.0055241073,0.8871069,0.015688146,0.08126865],"study_design_scores_gemma":[0.0008824455,0.00012533179,0.0007344152,0.00031378143,0.00004487769,0.0001478386,0.00062297867,0.000061796825,0.019190779,0.9740449,0.0037073132,0.00012351989],"about_ca_topic_score_codex":0.000003136241,"about_ca_topic_score_gemma":0.0000036169884,"teacher_disagreement_score":0.086938016,"about_ca_system_score_codex":0.00004775268,"about_ca_system_score_gemma":0.00004073027,"threshold_uncertainty_score":0.9946089},"labels":[],"label_agreement":null},{"id":"W2145644873","doi":"10.1142/s1793042113500292","title":"EULER PRODUCTS IN RAMANUJAN'S LOST NOTEBOOK","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"National Research Foundation of Korea","keywords":"Ramanujan's sum; Mathematics; Ramanujan tau function; Arithmetic function; Euler's formula; Mathematical proof; Pure mathematics; Modular form; Sketch; Ramanujan theta function; Dirichlet series; Algebra over a field; Arithmetic; Discrete mathematics; Dirichlet distribution; Algorithm; Mathematical analysis","score_opus":0.0314863558170211,"score_gpt":0.3286930005312351,"score_spread":0.29720664471421404,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2145644873","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7592974,0.00021368712,0.025855517,0.0056852303,0.0042343065,0.0007587784,0.000042145577,0.0000772324,0.20383574],"genre_scores_gemma":[0.89832973,0.000037826496,0.062052008,0.00040554596,0.0011652795,0.00002264354,0.0000038145756,0.000068884314,0.037914284],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99837667,0.00010524087,0.0006590845,0.0001126127,0.00057385693,0.0001725303],"domain_scores_gemma":[0.9971709,0.0014093278,0.0004169688,0.00016426021,0.0007746051,0.00006392291],"candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.00061390817,0.00013208126,0.00025141175,0.00016064971,0.000015191891,0.00007950639,0.0005247548,0.000053899545,0.0121470895],"category_scores_gemma":[0.0035510538,0.000106612286,0.00009891718,0.00007347646,0.0001029642,0.0006737136,0.0001030378,0.0002848444,0.0011827955],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0001428107,0.00069134124,0.0007741955,0.00009976474,0.00029670625,0.00028985785,0.001843982,0.000020756552,0.0017940382,0.9202893,0.06990327,0.0038539893],"study_design_scores_gemma":[0.0004900813,0.000017074291,0.00041780516,0.00025120104,0.000013454991,0.00032496997,0.00032888917,0.00001945631,0.0017307657,0.9929439,0.003349023,0.00011342564],"about_ca_topic_score_codex":0.0000045214338,"about_ca_topic_score_gemma":0.0000031942877,"teacher_disagreement_score":0.16592146,"about_ca_system_score_codex":0.00013885382,"about_ca_system_score_gemma":0.000054974204,"threshold_uncertainty_score":0.9995949},"labels":[],"label_agreement":null},{"id":"W2149054972","doi":"10.1142/s1793042112501254","title":"ON MODULAR GALOIS REPRESENTATIONS MODULO PRIME POWERS","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Simon Fraser University","funders":"Natural Sciences and Engineering Research Council of Canada; Danmarks Frie Forskningsfond; Deutsche Forschungsgemeinschaft","keywords":"Mathematics; Modulo; Galois module; Prime (order theory); Modular form; Splitting of prime ideals in Galois extensions; Pure mathematics; Galois extension; Galois group; Primitive root modulo n; Algebra over a field; Arithmetic; Normal basis; Discrete mathematics; Combinatorics","score_opus":0.02633468474805074,"score_gpt":0.34157264999004205,"score_spread":0.3152379652419913,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2149054972","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9007685,0.000104737774,0.026941901,0.0006835198,0.0039002649,0.00012497281,0.00006778657,0.000050112016,0.06735818],"genre_scores_gemma":[0.9913648,0.000014094026,0.0035808042,0.00045598162,0.0010320806,0.000004645228,0.000010160431,0.000034735724,0.0035027177],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99787307,0.0003132559,0.00058418134,0.00012823656,0.0008364301,0.00026480443],"domain_scores_gemma":[0.99664253,0.0019054277,0.0005550017,0.0002805949,0.0004288762,0.00018755962],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001757039,0.00017477316,0.0002447379,0.000223857,0.00006665065,0.000042864285,0.0005997822,0.000090333575,0.009785687],"category_scores_gemma":[0.0022784697,0.00014821123,0.00028522252,0.00013747167,0.000097548924,0.00055186846,0.00008401641,0.00036164912,0.00050522294],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0005086612,0.000774246,0.0025552274,0.000007864989,0.0007568186,0.00006018223,0.0017104003,0.00004228779,0.0004824206,0.9693345,0.021081995,0.002685409],"study_design_scores_gemma":[0.0007432204,0.000049188067,0.00241619,0.0001021975,0.00006755567,0.0007396111,0.00070214015,0.00001308337,0.0029813931,0.9859696,0.006034738,0.00018105432],"about_ca_topic_score_codex":0.0000024687042,"about_ca_topic_score_gemma":2.1280925e-7,"teacher_disagreement_score":0.09059626,"about_ca_system_score_codex":0.00015087675,"about_ca_system_score_gemma":0.000046107583,"threshold_uncertainty_score":0.9911195},"labels":[],"label_agreement":null},{"id":"W2149204921","doi":"10.1142/s1793042114500560","title":"The 3-adic eigencurve at the boundary of weight space","year":2014,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":31,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Mathematics; Boundary (topology); Quotient; Countable set; Pure mathematics; Space (punctuation); Buzzard; Upper and lower bounds; Combinatorics; Discrete mathematics; Mathematical analysis","score_opus":0.013716734844616512,"score_gpt":0.29376952250110244,"score_spread":0.28005278765648595,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2149204921","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.84901404,0.0013322792,0.021977494,0.0069471216,0.00607582,0.00022704907,0.00008136559,0.000033893524,0.11431094],"genre_scores_gemma":[0.9873041,0.00011978398,0.000515733,0.00032856732,0.0009678351,0.000003718689,0.0000033195774,0.000027624788,0.010729337],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9974202,0.00070630445,0.0006900221,0.00011333572,0.0008682153,0.0002019416],"domain_scores_gemma":[0.9906615,0.007362318,0.0009664801,0.00036629286,0.0005688176,0.00007459758],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0048289443,0.0001581726,0.000246043,0.00007041176,0.00024348866,0.000060659837,0.0012450017,0.00007276845,0.0043259235],"category_scores_gemma":[0.0024842334,0.00008293498,0.00031982333,0.00012572084,0.0005479284,0.00015787424,0.00021717037,0.000359916,0.00015546707],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00058815355,0.00011949002,0.0013683122,0.000012963441,0.0006153294,0.000018130188,0.0010102146,0.0000053019394,0.00024449223,0.94356006,0.03997971,0.012477846],"study_design_scores_gemma":[0.00039458918,0.000043364966,0.00061001425,0.00007462913,0.000055025186,0.0005716843,0.00038701735,0.000010378875,0.0027856978,0.8005019,0.19447981,0.00008589181],"about_ca_topic_score_codex":0.0000033534486,"about_ca_topic_score_gemma":0.0000091404445,"teacher_disagreement_score":0.1545001,"about_ca_system_score_codex":0.000102553815,"about_ca_system_score_gemma":0.000087420485,"threshold_uncertainty_score":0.99658424},"labels":[],"label_agreement":null},{"id":"W2152115950","doi":"10.1142/s1793042113500620","title":"THE NON-CYCLOTOMIC PART OF f(x)x<sup>n</sup>+ g(x) AND ROOTS OF RECIPROCAL POLYNOMIALS OFF THE UNIT CIRCLE","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Northern British Columbia","funders":"","keywords":"Mathematics; Cyclotomic polynomial; Reciprocal; Combinatorics; Unit circle; Unit (ring theory); Polynomial; Degree (music); Discriminant; Zero (linguistics); Bounded function; Factorization; Prime (order theory); Irreducible polynomial; Root of unity; Mathematical analysis; Physics","score_opus":0.0173464107725081,"score_gpt":0.28770201858047695,"score_spread":0.27035560780796886,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2152115950","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9919184,0.00027141135,0.00051239936,0.0010376173,0.00046145378,0.00020226487,0.000036596964,0.000007158482,0.005552688],"genre_scores_gemma":[0.99758583,0.00016765058,0.00029906826,0.00016598351,0.0004464674,0.000010538302,0.0000020661714,0.000024921435,0.0012974933],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9976003,0.00043297146,0.0010185497,0.00012427372,0.00061990466,0.00020400662],"domain_scores_gemma":[0.9925188,0.005276866,0.0010759487,0.0003098452,0.0007311776,0.00008739425],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0027213385,0.00016496936,0.00036656344,0.00009758936,0.00010815246,0.000056808494,0.00095311884,0.00009570163,0.0018811957],"category_scores_gemma":[0.0014850671,0.00009936311,0.00022291882,0.00012838043,0.00052180426,0.00026730518,0.0001858988,0.00034422785,0.000048441343],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.004316575,0.0017043552,0.02365683,0.0002586199,0.0071580047,0.00008287897,0.01164198,0.00024512934,0.0074067297,0.62072295,0.08609429,0.23671168],"study_design_scores_gemma":[0.0012239979,0.00012019246,0.013754672,0.00034363996,0.00012611192,0.0006545832,0.00365098,0.0001463677,0.005058211,0.96617585,0.008563655,0.00018175188],"about_ca_topic_score_codex":0.00001880052,"about_ca_topic_score_gemma":0.0000027852518,"teacher_disagreement_score":0.3454529,"about_ca_system_score_codex":0.000035826833,"about_ca_system_score_gemma":0.000102757236,"threshold_uncertainty_score":0.99903125},"labels":[],"label_agreement":null},{"id":"W2152421008","doi":"10.1142/s179304211250131x","title":"SIMPLE ZEROS OF MAASS L-FUNCTIONS","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"University of Rochester","keywords":"Simple (philosophy); Mathematics; Zero (linguistics); Function (biology); Pure mathematics","score_opus":0.057309545204154995,"score_gpt":0.3927377905592048,"score_spread":0.33542824535504984,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2152421008","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.84502226,0.00014572224,0.07365913,0.00047493703,0.0023057165,0.00017024328,0.00024302688,0.000036282632,0.0779427],"genre_scores_gemma":[0.99147695,0.000010718208,0.0022359425,0.00007919326,0.0008692138,0.0000028308204,0.0000071084364,0.000027939954,0.005290087],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99780834,0.00027994823,0.00067291484,0.000076793294,0.0009151014,0.00024691437],"domain_scores_gemma":[0.9962488,0.0019059707,0.00058118155,0.00020959368,0.0008943143,0.00016017469],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0024482391,0.00012025265,0.00027209477,0.00017728523,0.000037854978,0.000023399778,0.0006253565,0.000067385394,0.015915103],"category_scores_gemma":[0.0017699857,0.00009804051,0.00027310476,0.00012386216,0.00015229847,0.00040157803,0.00012804614,0.00030681244,0.0002522894],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0005351744,0.0009264948,0.036758658,0.00003138078,0.0013298101,0.000035972254,0.0011060636,0.000009413601,0.0018300848,0.89587474,0.05763338,0.0039288304],"study_design_scores_gemma":[0.00077015185,0.000048189253,0.0020731129,0.0000905994,0.00010410105,0.0007187969,0.001242274,0.000018656327,0.0029678268,0.9680837,0.023746023,0.00013658998],"about_ca_topic_score_codex":0.0000051953502,"about_ca_topic_score_gemma":9.877607e-7,"teacher_disagreement_score":0.14645472,"about_ca_system_score_codex":0.00012893762,"about_ca_system_score_gemma":0.0000908474,"threshold_uncertainty_score":0.98498446},"labels":[],"label_agreement":null},{"id":"W2152971985","doi":"10.1142/s1793042110003770","title":"AN EFFICIENT SEVENTH POWER RESIDUE SYMBOL ALGORITHM","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Cryptography and Data Security","field":"Computer Science","cited_by":9,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Mathematics; Legendre symbol; Quadratic residue; Reciprocity law; Cryptosystem; Euclidean algorithm; Cryptography; Residue (chemistry); Cyclotomic field; Residue field; Discrete mathematics; Arithmetic; Field (mathematics); Algorithm; Pure mathematics; Quadratic field; Quadratic equation","score_opus":0.003873487800447853,"score_gpt":0.2709308740261409,"score_spread":0.2670573862256931,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2152971985","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.2103823,0.00002987287,0.7805521,0.0005013479,0.004969513,0.000048429247,0.00011834466,0.000041888754,0.003356211],"genre_scores_gemma":[0.921468,0.000005388575,0.077635765,0.00038738557,0.00046872752,0.0000012485375,0.000009306962,0.000007665843,0.000016492695],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9985033,0.00012741,0.00034857486,0.0001777921,0.00068615424,0.00015673108],"domain_scores_gemma":[0.9984644,0.00020965378,0.00027485614,0.0003705136,0.00051892723,0.0001616588],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0011033567,0.00011082781,0.00012647099,0.00017601659,0.000058972182,0.00022385005,0.0020876909,0.000064240245,0.0014983461],"category_scores_gemma":[0.00010539468,0.00009246929,0.00015671646,0.00014206624,0.00008189789,0.00067707576,0.00016348065,0.0004461352,0.00006931835],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00009648935,0.00084407534,0.0013554438,0.0000017787106,0.00018229679,0.00040917462,0.0018721669,0.00009143919,0.00169516,0.92058676,0.004893259,0.06797194],"study_design_scores_gemma":[0.0029131568,0.000442813,0.04553363,0.00016499411,0.00004682472,0.008140727,0.00064617733,0.017180169,0.006434564,0.82715595,0.09041172,0.00092926703],"about_ca_topic_score_codex":0.0000075006387,"about_ca_topic_score_gemma":0.0000054930765,"teacher_disagreement_score":0.71108574,"about_ca_system_score_codex":0.00002239658,"about_ca_system_score_gemma":0.00009275307,"threshold_uncertainty_score":0.99941444},"labels":[],"label_agreement":null},{"id":"W2155788403","doi":"10.1142/s1793042114500535","title":"Counting squarefree values of polynomials with error term","year":2014,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Square-free integer; Term (time); Asymptotic formula; Conjecture; Combinatorics; Elliott–Halberstam conjecture; Discrete mathematics; Collatz conjecture","score_opus":0.02164249868147407,"score_gpt":0.3140718707701445,"score_spread":0.2924293720886704,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2155788403","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9620966,0.000034680983,0.014189954,0.000217511,0.00070901884,0.000063987456,0.000033034863,0.000019889127,0.022635369],"genre_scores_gemma":[0.9917387,0.0000047811695,0.0063468954,0.00016369937,0.00072833605,0.0000017743314,0.0000037897128,0.00003015464,0.0009818972],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9979554,0.0002898955,0.0007257349,0.00012156366,0.000739655,0.00016778748],"domain_scores_gemma":[0.9955651,0.0022565324,0.0011642826,0.00021284346,0.00072479324,0.00007642343],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0025284297,0.00016365299,0.0003811133,0.00016905103,0.00004326225,0.00003610356,0.0006897494,0.00007371753,0.0032512033],"category_scores_gemma":[0.0013457511,0.000119814045,0.00018342464,0.0000847538,0.00018689553,0.000285468,0.00007698573,0.00023119508,0.000044029377],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0028399054,0.00081890094,0.028760912,0.00015248607,0.0021812124,0.00011121402,0.0034033852,0.00004391632,0.003030611,0.9318479,0.009373794,0.017435793],"study_design_scores_gemma":[0.0015557813,0.00019531538,0.0035081904,0.00052745047,0.00013515558,0.0009507521,0.00084728724,0.000022347009,0.006855334,0.98282284,0.0023639966,0.00021554694],"about_ca_topic_score_codex":0.0000034478646,"about_ca_topic_score_gemma":0.0000015154541,"teacher_disagreement_score":0.050974973,"about_ca_system_score_codex":0.000054589855,"about_ca_system_score_gemma":0.000069319525,"threshold_uncertainty_score":0.99766},"labels":[],"label_agreement":null},{"id":"W2162552769","doi":"10.1142/s179304211450033x","title":"Representations by certain octonary quadratic forms with coefficients 1, 3 or 9","year":2014,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Pure mathematics; Quadratic equation; Geometry","score_opus":0.03370123879334183,"score_gpt":0.37832365797875256,"score_spread":0.3446224191854107,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2162552769","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.32933983,0.000039829116,0.5437532,0.002561711,0.0006495672,0.00042514756,0.00018983085,0.000082508115,0.12295837],"genre_scores_gemma":[0.9768761,0.000009427678,0.0045756823,0.00034002218,0.00023937409,0.000010224293,0.000025688729,0.00004917425,0.017874343],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99717236,0.00042255208,0.0006642165,0.00018411268,0.0012963722,0.00026041578],"domain_scores_gemma":[0.99472255,0.003452953,0.0005345016,0.000291371,0.00082423806,0.00017440498],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0019097069,0.00017984363,0.0003073408,0.00016940694,0.00008855426,0.000101777354,0.0008823791,0.000065445536,0.0073808925],"category_scores_gemma":[0.00222574,0.00011256176,0.00014562086,0.00019324184,0.0002152295,0.00035055686,0.00010274243,0.0003404831,0.00015427578],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.005159929,0.0016853116,0.0063767605,0.000067787456,0.0020559859,0.00045111892,0.0020175958,0.0001445557,0.0005593451,0.8322864,0.13508245,0.014112753],"study_design_scores_gemma":[0.0030751843,0.0003976168,0.0002497921,0.00037395157,0.00014130892,0.0024156834,0.0024276436,0.0008335824,0.000926293,0.95119405,0.037617072,0.0003478286],"about_ca_topic_score_codex":0.0000072769485,"about_ca_topic_score_gemma":0.000011265961,"teacher_disagreement_score":0.6475362,"about_ca_system_score_codex":0.0001501171,"about_ca_system_score_gemma":0.00015757578,"threshold_uncertainty_score":0.9935265},"labels":[],"label_agreement":null},{"id":"W2163657101","doi":"10.1142/s1793042106000474","title":"A GENERALIZATION OF A THEOREM OF BUMBY ON QUARTIC DIOPHANTINE EQUATIONS","year":2006,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":11,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Ottawa; University of British Columbia","funders":"","keywords":"Diophantine equation; Mathematics; Integer (computer science); Quartic function; Generalization; Quartic surface; Diophantine set; Legendre's equation; Thue equation; Discrete mathematics; Pure mathematics; Combinatorics; Mathematical analysis","score_opus":0.008623245802747722,"score_gpt":0.25760032814902345,"score_spread":0.24897708234627572,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2163657101","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.29180533,0.000040796767,0.70480394,0.00051006064,0.0006025,0.00003753074,0.000014680066,0.000010142929,0.0021749875],"genre_scores_gemma":[0.9947057,0.0000042998117,0.0047626826,0.00009274701,0.0002713842,0.0000010811699,0.000007346064,0.000005074409,0.00014970644],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99867487,0.00012380825,0.0005632959,0.000087304834,0.00047200426,0.000078719495],"domain_scores_gemma":[0.99822915,0.0004167456,0.0006802112,0.00011607204,0.0005302564,0.000027581],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00046659505,0.000074683514,0.0001483003,0.00018087185,0.000020233441,0.00002881264,0.00056008395,0.000026799838,0.00014212808],"category_scores_gemma":[0.00015973175,0.000061982966,0.00012428705,0.0001780934,0.000056382498,0.00028072068,0.000053095217,0.00006572496,0.000010602609],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0000854195,0.00025139586,0.0003785798,0.0000045949373,0.00006487659,0.000008959983,0.00028455825,0.005220196,0.0077400017,0.9707598,0.00053348613,0.014668151],"study_design_scores_gemma":[0.001336882,0.00022647306,0.009021672,0.00023341127,0.000026932228,0.000119632554,0.000040929866,0.03180333,0.041329764,0.91504216,0.0006619078,0.0001569063],"about_ca_topic_score_codex":0.000020347867,"about_ca_topic_score_gemma":0.0000025004654,"teacher_disagreement_score":0.70290035,"about_ca_system_score_codex":0.000034049037,"about_ca_system_score_gemma":0.00007702794,"threshold_uncertainty_score":0.2527592},"labels":[],"label_agreement":null},{"id":"W2164529357","doi":"10.1142/s1793042106000541","title":"ON THE DISTRIBUTION OF CYCLIC CUBIC FIELDS WITH INDEX 2","year":2006,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Algebraic number field; Distribution (mathematics); Index (typography); Field (mathematics); Asymptotic formula; Pure mathematics; Combinatorics; Discrete mathematics; Mathematical analysis","score_opus":0.021354426816902312,"score_gpt":0.32483144887413157,"score_spread":0.30347702205722926,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2164529357","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.913086,0.00001559032,0.057256825,0.0015334858,0.00020103974,0.00009744465,0.000066937704,0.0000102744825,0.027732417],"genre_scores_gemma":[0.9975224,0.0000040681516,0.0001572168,0.000097491036,0.0002757259,0.0000030132383,0.0000097151,0.000014954424,0.0019153825],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99813515,0.00024496485,0.0004550051,0.00008518086,0.0009410425,0.00013868121],"domain_scores_gemma":[0.99574035,0.0029256667,0.0004860452,0.00019668434,0.0006130032,0.00003822861],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0013202785,0.00010880499,0.00018889962,0.000072122355,0.00004060832,0.000032892247,0.0006112415,0.000058736237,0.002899625],"category_scores_gemma":[0.0007568337,0.00006179407,0.00014495628,0.00011938246,0.00019117747,0.000106606516,0.00005298723,0.00035441262,0.000036331603],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00073838705,0.0002677715,0.0030975805,0.000007744195,0.00028865703,0.00005896466,0.00009515231,0.00013586953,0.000053376036,0.974447,0.020234406,0.000575064],"study_design_scores_gemma":[0.00056100206,0.000085753054,0.0021232439,0.00016977069,0.00003144392,0.00027938886,0.0001912791,0.00010085795,0.0012363569,0.993958,0.0011887742,0.00007411704],"about_ca_topic_score_codex":0.000018414446,"about_ca_topic_score_gemma":0.000009947318,"teacher_disagreement_score":0.08443645,"about_ca_system_score_codex":0.000102609214,"about_ca_system_score_gemma":0.00007803554,"threshold_uncertainty_score":0.9980119},"labels":[],"label_agreement":null},{"id":"W2165650422","doi":"10.1142/s179304211000279x","title":"FOURTEEN OCTONARY QUADRATIC FORMS","year":2010,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Diagonal; Quadratic equation; Integer (computer science); Pure mathematics; Convolution (computer science); Quadratic function; Function (biology); Binary quadratic form; Divisor function; Combinatorics; Divisor (algebraic geometry); Geometry","score_opus":0.034755288852813274,"score_gpt":0.382782784553356,"score_spread":0.34802749570054275,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2165650422","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8465586,0.00002566122,0.014520856,0.002016438,0.0027146745,0.00018022553,0.00006775301,0.0000567881,0.13385902],"genre_scores_gemma":[0.9823363,0.000009498421,0.009211104,0.00026506308,0.0011570553,0.0000048004554,0.000006436493,0.000045404682,0.0069643827],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9975216,0.00018378123,0.00072269846,0.00014340515,0.0011649258,0.00026361048],"domain_scores_gemma":[0.99574554,0.0023238123,0.00052601326,0.0003023312,0.00091293757,0.00018933609],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002673219,0.00017271761,0.0003011274,0.00020587382,0.00006077838,0.00009355465,0.0012719535,0.000114030976,0.022707649],"category_scores_gemma":[0.0025962074,0.00013001433,0.0003058056,0.000114664224,0.00020719596,0.00045317283,0.00016527431,0.00088505313,0.0004625452],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00042367214,0.00034628357,0.0029282838,0.000016102367,0.00068176,0.0004299246,0.00057339924,0.0000015500658,0.0019215224,0.9623952,0.021636529,0.0086457655],"study_design_scores_gemma":[0.0007061471,0.00004563478,0.0005034463,0.00006955722,0.00004779926,0.0023637642,0.00040532785,0.00006793233,0.00076491694,0.9798644,0.015012027,0.0001490464],"about_ca_topic_score_codex":0.0000032458142,"about_ca_topic_score_gemma":0.000011915171,"teacher_disagreement_score":0.13577768,"about_ca_system_score_codex":0.00008655198,"about_ca_system_score_gemma":0.00019256577,"threshold_uncertainty_score":0.9781857},"labels":[],"label_agreement":null},{"id":"W2167958081","doi":"10.1142/s1793042114500171","title":"Analogues of Ramanujan's 24 squares formula","year":2014,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Ramanujan's sum; Mathematics; Ramanujan tau function; Combinatorics; Ramanujan theta function; Integer (computer science); Divisor function; Class (philosophy); Pure mathematics; Divisor (algebraic geometry)","score_opus":0.03094206815979081,"score_gpt":0.3544654712320555,"score_spread":0.3235234030722647,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2167958081","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.3840921,0.00018716374,0.524199,0.0005589517,0.002482076,0.00018539849,0.000111208894,0.000068937596,0.08811514],"genre_scores_gemma":[0.9673243,0.00002217141,0.028630562,0.000087741435,0.0004512589,0.0000023686523,0.0000041583553,0.000025611067,0.0034518032],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9983336,0.00012369994,0.0007039523,0.00007768084,0.0006379917,0.00012308224],"domain_scores_gemma":[0.9960331,0.0023243986,0.0007429407,0.0001605769,0.00067862385,0.000060380382],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008977456,0.00011619788,0.00031666388,0.00013850359,0.000021196913,0.000031701442,0.0005533508,0.000051659197,0.0017278043],"category_scores_gemma":[0.0032315457,0.0000913315,0.00022177628,0.000052211864,0.00013315037,0.000335144,0.00008863823,0.00016685145,0.000042840275],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00011858055,0.00018871203,0.00025488908,0.00006143201,0.00026632228,0.00001867614,0.0005790731,0.000019665236,0.000491276,0.9870374,0.0091888895,0.0017750444],"study_design_scores_gemma":[0.00044720658,0.00005356961,0.00013541005,0.00026158226,0.000045493874,0.0001820629,0.00035760138,0.00007297097,0.0037867245,0.99026376,0.0043059387,0.000087675435],"about_ca_topic_score_codex":0.0000017688412,"about_ca_topic_score_gemma":0.0000031016352,"teacher_disagreement_score":0.5832322,"about_ca_system_score_codex":0.000049711387,"about_ca_system_score_gemma":0.000026553018,"threshold_uncertainty_score":0.9991847},"labels":[],"label_agreement":null},{"id":"W2168442202","doi":"10.1142/s1793042114500092","title":"Equivariant functions and vector-valued modular forms","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Ottawa","funders":"","keywords":"Equivariant map; Mathematics; Monodromy; Parameterized complexity; Modular form; Modular design; Pure mathematics; Algebra over a field; Representation (politics); Vector bundle; Differential (mechanical device); Discrete group; Group (periodic table); Combinatorics; Computer science","score_opus":0.019137632333200975,"score_gpt":0.3101730200012488,"score_spread":0.2910353876680478,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2168442202","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8822943,0.0001033664,0.104047164,0.0007652586,0.0010487948,0.000100221594,0.000031492058,0.0000248618,0.011584558],"genre_scores_gemma":[0.99157846,0.000015086182,0.0055672997,0.00018705298,0.00041235535,0.0000052186283,0.000003925596,0.000017269083,0.002213358],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99903756,0.000049219994,0.00035201843,0.00008565899,0.0003513331,0.00012418843],"domain_scores_gemma":[0.9986786,0.00043210544,0.00027682693,0.00010474921,0.0004184441,0.000089262125],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00034778772,0.00009979354,0.00015822737,0.000108838365,0.000044144595,0.000061006158,0.0002282329,0.00004781949,0.0052702874],"category_scores_gemma":[0.00060584745,0.000073382485,0.00010231944,0.00006436157,0.00005810452,0.0004960347,0.00007069317,0.00018598355,0.0001441807],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00008717024,0.00015770018,0.0006279359,0.000011258595,0.00045363625,0.00004938895,0.00028989234,0.000017645056,0.0013924309,0.9772512,0.0067927325,0.012869034],"study_design_scores_gemma":[0.000516345,0.000038133636,0.0024658702,0.000058016132,0.000028427748,0.000640141,0.00040430974,0.00009571479,0.00022771583,0.99362934,0.0018046777,0.000091339534],"about_ca_topic_score_codex":0.0000016217991,"about_ca_topic_score_gemma":6.4447545e-7,"teacher_disagreement_score":0.109284155,"about_ca_system_score_codex":0.00005107197,"about_ca_system_score_gemma":0.00002686151,"threshold_uncertainty_score":0.995639},"labels":[],"label_agreement":null},{"id":"W2168989363","doi":"10.1142/s1793042108001195","title":"ON DAVENPORT'S CONSTANT","year":2008,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Exponent; Constant (computer programming); Sequence (biology); Combinatorics; Abelian group; Group (periodic table); Upper and lower bounds; Discrete mathematics; Mathematical analysis; Physics","score_opus":0.03471486967437191,"score_gpt":0.3272558679075407,"score_spread":0.29254099823316876,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2168989363","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8409474,0.00005074126,0.0029032715,0.00028698286,0.0030399633,0.000060034003,0.000068510475,0.000025891655,0.15261723],"genre_scores_gemma":[0.99507815,0.000046981615,0.0024407145,0.00062276406,0.0005046889,9.856976e-7,0.0000021676603,0.000018211322,0.0012853692],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99859077,0.00012494555,0.0004581895,0.00008829907,0.0006197854,0.000117987816],"domain_scores_gemma":[0.99761367,0.0013499946,0.00042772095,0.00015359203,0.00038155334,0.00007345681],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005933867,0.000116864496,0.00019769484,0.00011943116,0.00009493115,0.000015035786,0.0004977324,0.000056838973,0.005798281],"category_scores_gemma":[0.00094922783,0.00008372728,0.00021130375,0.000046468616,0.00019348848,0.00011868885,0.00006375273,0.00027087002,0.00003493931],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0003795999,0.00010914582,0.0006293102,0.0000025858535,0.00027097214,0.00074110704,0.0007287654,0.0000045742777,0.00003823178,0.9647322,0.030993747,0.0013697401],"study_design_scores_gemma":[0.0005659206,0.000056645982,0.00045581497,0.00007329075,0.000017879462,0.0040245703,0.00010662701,0.000003132475,0.00033291633,0.98400426,0.010264148,0.000094777075],"about_ca_topic_score_codex":5.0912047e-7,"about_ca_topic_score_gemma":2.4131572e-7,"teacher_disagreement_score":0.15413074,"about_ca_system_score_codex":0.000058063128,"about_ca_system_score_gemma":0.00006231187,"threshold_uncertainty_score":0.9951106},"labels":[],"label_agreement":null},{"id":"W2169915269","doi":"10.1142/s1793042112500984","title":"A PROBLEM OF FOMENKO'S RELATED TO ARTIN'S CONJECTURE","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Conjecture; Riemann hypothesis; Constant (computer programming); Combinatorics; Prime (order theory); Value (mathematics); Pure mathematics; Statistics","score_opus":0.033061971636820654,"score_gpt":0.38242088984504574,"score_spread":0.34935891820822507,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2169915269","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8947697,0.00013370262,0.010521586,0.0021284996,0.00095824024,0.0003236758,0.00008278192,0.00003576412,0.09104602],"genre_scores_gemma":[0.9820931,0.0000058614824,0.011463635,0.00015643977,0.000321617,0.000005069494,0.0000030536698,0.00003446031,0.005916759],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99747705,0.00032356213,0.0008375451,0.0001004109,0.00096725294,0.00029418443],"domain_scores_gemma":[0.9966875,0.0014406398,0.00063323247,0.00019600883,0.0008060988,0.00023655336],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0031250427,0.00014638442,0.00033803965,0.00023118303,0.00002639059,0.000025020496,0.0006923964,0.00009182544,0.01153305],"category_scores_gemma":[0.0012672684,0.00011446473,0.0002303978,0.00020097644,0.00010558873,0.00028501204,0.00015391682,0.00037302406,0.00027720808],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0006646664,0.0005988625,0.0075399536,0.00003801205,0.0011300803,0.000065407534,0.0045687635,0.000018685509,0.0018368433,0.9489367,0.028580025,0.0060219937],"study_design_scores_gemma":[0.00082572456,0.0000932827,0.00062035944,0.00025542945,0.00007071976,0.0009100936,0.0007568858,0.000008417694,0.0030476397,0.9738854,0.019376725,0.00014930216],"about_ca_topic_score_codex":0.0000024907388,"about_ca_topic_score_gemma":8.655431e-7,"teacher_disagreement_score":0.087323375,"about_ca_system_score_codex":0.00014476413,"about_ca_system_score_gemma":0.00009834803,"threshold_uncertainty_score":0.9893705},"labels":[],"label_agreement":null},{"id":"W2171433699","doi":"10.1142/s1793042112500674","title":"A FAMILY OF GENERALIZED KAC–MOODY ALGEBRAS AND DEFORMATION OF MODULAR FORMS","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Ramanujan's sum; Mathematics; Modular form; Diagonal; Pure mathematics; Modular design; Deformation (meteorology); Algebra over a field; Function (biology); Theta function; Ramanujan theta function; Geometry","score_opus":0.031054182827683855,"score_gpt":0.33784537571706547,"score_spread":0.3067911928893816,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2171433699","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9572809,0.00022858907,0.03795679,0.000040380568,0.0002720023,0.000071921546,0.000028919963,0.0000074114087,0.0041130846],"genre_scores_gemma":[0.96999514,0.00006563521,0.029486096,0.000036667352,0.00013355578,0.000002582769,0.0000033936683,0.000015999733,0.00026094224],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99847895,0.00005173094,0.0007709002,0.00004600656,0.0005318528,0.00012053062],"domain_scores_gemma":[0.9980125,0.0004315895,0.00088835735,0.000107882755,0.0004942978,0.0000653668],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008580174,0.00010150192,0.00029919672,0.00012472685,0.00001571382,0.000013186151,0.00023822421,0.000051387025,0.00038290743],"category_scores_gemma":[0.00060299714,0.00007666855,0.00013251277,0.00004925128,0.000111272806,0.0007921403,0.0000791474,0.00010485552,0.0000068645013],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00014345656,0.00023949341,0.0012642867,0.00011886259,0.00032743526,0.0000031212637,0.0018035647,0.000012616291,0.005799462,0.98908556,0.00039672572,0.00080544717],"study_design_scores_gemma":[0.00065119605,0.000031403324,0.0014627333,0.00019727083,0.0000627028,0.0002073007,0.0007723951,0.00007593196,0.01040866,0.98588073,0.00017417899,0.00007546455],"about_ca_topic_score_codex":0.0000027504743,"about_ca_topic_score_gemma":5.9013894e-7,"teacher_disagreement_score":0.012714226,"about_ca_system_score_codex":0.00004603278,"about_ca_system_score_gemma":0.000023324488,"threshold_uncertainty_score":0.41925678},"labels":[],"label_agreement":null},{"id":"W2182361844","doi":"10.1142/s1793042112501485","title":"OMEGA THEOREMS FOR $\\frac{L'}{L}(1, \\chi_D)$","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Dirichlet distribution; Combinatorics; Omega; Algebraic number field; Class number formula; Analytic number theory; Quadratic field; Pure mathematics; Quadratic equation; Dirichlet series; Mathematical analysis; Quadratic function; Geometry; Quantum mechanics","score_opus":0.07009748560296154,"score_gpt":0.41576730482600904,"score_spread":0.3456698192230475,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2182361844","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.44103593,0.000677159,0.34343877,0.0033540232,0.009498032,0.00093694625,0.00050953915,0.00014715153,0.20040244],"genre_scores_gemma":[0.974644,0.000022687344,0.013391991,0.00034995234,0.0031929433,0.000017646136,0.000011437593,0.000066871406,0.00830247],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9974122,0.00031327739,0.0007336171,0.0001288023,0.00096958893,0.00044248573],"domain_scores_gemma":[0.99325156,0.0046222485,0.00057916925,0.0002558502,0.0010407977,0.00025035228],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0049751406,0.00019496267,0.00034885624,0.0002069792,0.00007313299,0.00007467722,0.0010387393,0.00010404107,0.0065504396],"category_scores_gemma":[0.0035906455,0.00015214359,0.0004325159,0.00011221634,0.00017949851,0.00057600316,0.00013475273,0.00036040242,0.00024117582],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00080306124,0.00042988514,0.0023847297,0.000020821533,0.0007834024,0.000020912386,0.0010808998,0.0000018002025,0.00024566965,0.9466948,0.041062776,0.0064712716],"study_design_scores_gemma":[0.0010736515,0.000050190123,0.00021331264,0.000092913644,0.00008337546,0.0007622724,0.000746795,0.00002970809,0.0009642159,0.92601585,0.06979766,0.00017005793],"about_ca_topic_score_codex":0.0000012764074,"about_ca_topic_score_gemma":9.86347e-7,"teacher_disagreement_score":0.5336081,"about_ca_system_score_codex":0.00019699575,"about_ca_system_score_gemma":0.000109805085,"threshold_uncertainty_score":0.9943577},"labels":[],"label_agreement":null},{"id":"W2194693458","doi":"10.1142/s1793042112500972","title":"ON THE QUATERNARY FORMS x<sup>2</sup>+y<sup>2</sup>+2z<sup>2</sup>+3t<sup>2</sup>, x<sup>2</sup>+2y<sup>2</sup>+2z<sup>2</sup>+6t<sup>2</sup>, x<sup>2</sup>+3y<sup>2</sup>+3z<sup>2</sup>+6t<sup>2</sup> AND 2x<sup>2</sup>+3y<sup>2</sup>+6z<sup>2</sup>+6t<sup>2</sup>","year":2012,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Integer (computer science); Combinatorics; Physics; Crystallography; Chemistry; Mathematics","score_opus":0.02820047917843641,"score_gpt":0.30403344836497836,"score_spread":0.27583296918654193,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2194693458","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8160756,0.019504702,0.017974604,0.01745695,0.0062781144,0.0380784,0.03593786,0.014565274,0.03412846],"genre_scores_gemma":[0.79765636,0.014784381,0.025593488,0.018441843,0.03954805,0.01193866,0.01755882,0.018405888,0.056072533],"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","domain_scores_codex":[0.80894196,0.02643523,0.048751004,0.031169085,0.042797655,0.04190506],"domain_scores_gemma":[0.8464296,0.047826923,0.024789361,0.034014326,0.02110625,0.02583354],"candidate_categories":["metaresearch","metaepi_narrow","metaepi_broad","bibliometrics","sts","scholarly_communication","open_science","research_integrity","insufficient_payload"],"consensus_categories":["metaresearch","metaepi_narrow","metaepi_broad","bibliometrics","sts","scholarly_communication","open_science","research_integrity","insufficient_payload"],"category_scores_codex":[0.04587609,0.04551437,0.0434053,0.026541939,0.020555938,0.022282382,0.056323357,0.025218396,0.05332624],"category_scores_gemma":[0.038216576,0.04455945,0.030389324,0.024568258,0.025601849,0.043137506,0.028881684,0.051690686,0.03725232],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":true,"about_ca_system_consensus":true,"study_design_scores_codex":[0.019816961,0.024099968,0.009856327,0.009032745,0.030996658,0.011739877,0.09003444,0.5605045,0.00066761835,0.049871422,0.18215032,0.011229141],"study_design_scores_gemma":[0.046897035,0.0078742625,0.00038155817,0.017021675,0.01539887,0.026506798,0.10288908,0.4712591,0.0026474344,0.090545096,0.18297428,0.035604812],"about_ca_topic_score_codex":0.0060516912,"about_ca_topic_score_gemma":0.00044946917,"teacher_disagreement_score":0.08924542,"about_ca_system_score_codex":0.025851227,"about_ca_system_score_gemma":0.014855217,"threshold_uncertainty_score":0.99616504},"labels":[],"label_agreement":null},{"id":"W2196099892","doi":"10.1142/s1793042115501109","title":"Fourier coefficients of a class of eta quotients of weight 2","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Modular form; Fourier series; Quotient; Class (philosophy); Dedekind eta function; Kronecker delta; Pure mathematics; Eisenstein series; Algebra over a field; Mathematical analysis; Physics","score_opus":0.03769232301188259,"score_gpt":0.35095540098913725,"score_spread":0.31326307797725467,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2196099892","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.96614414,0.000098185796,0.023536468,0.0000771831,0.0010740032,0.000056986006,0.000113015114,0.00000405058,0.008895938],"genre_scores_gemma":[0.9934385,0.000010030557,0.005711524,0.000035706813,0.00013750335,5.624446e-7,0.000003694971,0.000014719441,0.0006477844],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9979381,0.00010336574,0.0008209274,0.00007429042,0.0009624721,0.00010085758],"domain_scores_gemma":[0.99622387,0.00058626046,0.0013305251,0.00015861135,0.0016180349,0.00008271741],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008164851,0.00009911154,0.0003381453,0.00020165944,0.00000760319,0.000004385034,0.0005001503,0.000058845562,0.00067465036],"category_scores_gemma":[0.0013817531,0.000078530364,0.00019026986,0.00013897018,0.00013914367,0.00015773159,0.000094849405,0.00014291608,0.000009810751],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0028282774,0.0034671663,0.034381058,0.00018655427,0.0022100164,0.000093944596,0.0046180324,0.00043566743,0.0029500576,0.9161842,0.01573435,0.016910667],"study_design_scores_gemma":[0.0024227505,0.00019092455,0.0008947927,0.00046793098,0.000089530244,0.00013972321,0.0007359533,0.00008399245,0.017360874,0.97307664,0.004416806,0.0001201022],"about_ca_topic_score_codex":0.0000011324672,"about_ca_topic_score_gemma":6.669044e-7,"teacher_disagreement_score":0.05689241,"about_ca_system_score_codex":0.000050691713,"about_ca_system_score_gemma":0.00010218311,"threshold_uncertainty_score":0.73869485},"labels":[],"label_agreement":null},{"id":"W2203709017","doi":"10.1142/s1793042116500950","title":"Representation numbers of certain quaternary quadratic forms in a genus consisting of a single class","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Discriminant; Genus; Class (philosophy); Pure mathematics; Representation (politics); Quadratic equation; Combinatorics; Quaternary; Class number; Geometry; Botany","score_opus":0.07281451272873132,"score_gpt":0.37395037211530574,"score_spread":0.3011358593865744,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2203709017","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9817508,0.00006619976,0.011484975,0.00014715694,0.00036582412,0.000073241405,0.000021573072,0.000006312562,0.006083927],"genre_scores_gemma":[0.99319124,0.0000051580623,0.006432595,0.00005151078,0.000102834674,0.000002080136,0.000005350539,0.000015903865,0.00019334066],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99804634,0.00017024184,0.000970983,0.00009576287,0.00059713697,0.000119518125],"domain_scores_gemma":[0.9966033,0.0013112167,0.0012105802,0.00013168564,0.00067585753,0.000067375884],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009970376,0.000105019426,0.00033826724,0.00023891017,0.000009418217,0.000011879923,0.00030059397,0.0000571811,0.00019649473],"category_scores_gemma":[0.0030766996,0.00008959141,0.0001404619,0.00019447051,0.000092261194,0.00031825868,0.000060191112,0.00015813125,0.000005938358],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0051270016,0.0032238392,0.23254102,0.0003633916,0.0017108318,0.0010254034,0.023713581,0.002329976,0.018338919,0.6719633,0.0039364477,0.03572634],"study_design_scores_gemma":[0.00171225,0.00012097464,0.0008762105,0.0004720695,0.00003620537,0.00045756856,0.0048412215,0.00026454031,0.006184898,0.9847483,0.00017133092,0.00011445248],"about_ca_topic_score_codex":0.00002262086,"about_ca_topic_score_gemma":0.000027641421,"teacher_disagreement_score":0.31278503,"about_ca_system_score_codex":0.0001405742,"about_ca_system_score_gemma":0.00010397749,"threshold_uncertainty_score":0.3683319},"labels":[],"label_agreement":null},{"id":"W2216864981","doi":"10.1142/s1793042111004988","title":"$\\mathbb{Q}(\\sqrt{2}, \\sqrt{35})$ HAS A NON-PRINCIPAL EUCLIDEAN IDEAL","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Principal ideal; Ideal (ethics); Euclidean geometry; Quartic function; Principal (computer security); Combinatorics; Euclidean distance; Euclidean domain; Quartic surface; Discrete mathematics; Euclidean distance matrix; Pure mathematics; Geometry; Computer science; Prime (order theory)","score_opus":0.06744439769146778,"score_gpt":0.3208979966081605,"score_spread":0.2534535989166927,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2216864981","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8226956,0.00010835385,0.025975157,0.00041549155,0.004177854,0.00021257828,0.000100373356,0.00010316211,0.14621139],"genre_scores_gemma":[0.9805732,0.000027343802,0.014447485,0.0004181205,0.0013183721,0.000008158357,0.000008906744,0.000073775176,0.0031246736],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.996627,0.00034008184,0.0012459371,0.0002760724,0.0010888488,0.0004221117],"domain_scores_gemma":[0.9960906,0.0013192346,0.0011277975,0.00040745284,0.0007683185,0.00028657724],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002794057,0.00035205839,0.0005348172,0.0003352691,0.00013425478,0.000111326815,0.001536313,0.0001935749,0.022353075],"category_scores_gemma":[0.0014202485,0.00030185404,0.0005322955,0.00020471291,0.0003112615,0.00058457133,0.0002884059,0.00069350004,0.00075313094],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.002754424,0.0015265584,0.005369941,0.00006876458,0.00244609,0.001926983,0.012084695,0.000004799797,0.00080367475,0.9237902,0.036395017,0.012828824],"study_design_scores_gemma":[0.0015128618,0.00013687077,0.0017584591,0.00028793205,0.00013692662,0.0028000681,0.0012209244,0.000022353786,0.0037291073,0.9734405,0.014586738,0.0003672587],"about_ca_topic_score_codex":0.000020425441,"about_ca_topic_score_gemma":0.0000063651723,"teacher_disagreement_score":0.15787752,"about_ca_system_score_codex":0.00016647087,"about_ca_system_score_gemma":0.00020592181,"threshold_uncertainty_score":0.9999434},"labels":[],"label_agreement":null},{"id":"W2220071148","doi":"10.1142/s1793042115500888","title":"On the pseudo-nullity of the dual fine Selmer groups","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Dual (grammatical number); Galois module; Galois group; Abelian group; Group (periodic table); Extension (predicate logic); Abelian extension; Prime (order theory)","score_opus":0.043280524645490454,"score_gpt":0.3117142430905447,"score_spread":0.26843371844505426,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2220071148","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.973484,0.00003092444,0.00088894664,0.0026163901,0.0017923812,0.000092531795,0.000054265387,0.000010272536,0.021030309],"genre_scores_gemma":[0.9964039,0.0000032377911,0.00037468813,0.0006346538,0.00055676245,0.000002758613,0.0000016688772,0.000018391134,0.0020039466],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9974828,0.0006107981,0.0006019367,0.00010237978,0.0010578361,0.00014426146],"domain_scores_gemma":[0.994715,0.0033779058,0.0007702697,0.00033444774,0.00072076917,0.000081634964],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0034807213,0.00014850292,0.00023303834,0.00006467712,0.000056843368,0.000028709519,0.0010001033,0.00007279045,0.0035969997],"category_scores_gemma":[0.0042553265,0.00007552843,0.00028751497,0.00015379654,0.00024440975,0.00014458591,0.0001748845,0.00045264672,0.00009225829],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0008016371,0.000320742,0.0009823381,0.000006928302,0.00040986584,0.00002516778,0.0013141449,0.000015457685,0.00013657346,0.9528392,0.042511735,0.00063622324],"study_design_scores_gemma":[0.00067166303,0.00005882261,0.0011639011,0.00012111402,0.00005168811,0.0005175981,0.0007342608,0.0000071438008,0.00354694,0.99069077,0.0023495795,0.00008649968],"about_ca_topic_score_codex":0.0000031567363,"about_ca_topic_score_gemma":0.0000021448027,"teacher_disagreement_score":0.040162154,"about_ca_system_score_codex":0.00008811149,"about_ca_system_score_gemma":0.00011914695,"threshold_uncertainty_score":0.99731386},"labels":[],"label_agreement":null},{"id":"W2231564461","doi":"10.1142/s1793042117500385","title":"Representations by octonary quadratic forms with coefficients 1, 2, 3 or 6","year":2016,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Modular form; Diagonal; Quadratic equation; Integer (computer science); Eisenstein series; Pure mathematics; Combinatorics; Algebra over a field; Geometry","score_opus":0.039037971244046676,"score_gpt":0.3848348243903643,"score_spread":0.34579685314631764,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2231564461","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.39979896,0.00006192131,0.52098393,0.0052489885,0.00074396114,0.00045407293,0.0005076143,0.00008908497,0.07211146],"genre_scores_gemma":[0.95905775,0.000027939037,0.0030680604,0.00020368035,0.0001992381,0.000010933579,0.000008695066,0.00004700844,0.03737668],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9974417,0.00024931305,0.00062854256,0.00017549652,0.0012549966,0.00024992533],"domain_scores_gemma":[0.9946456,0.0035376688,0.00050387316,0.00027085992,0.00087819604,0.00016380196],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0012271776,0.00016468964,0.00026315355,0.00015682934,0.00006633317,0.0000642704,0.0008346624,0.000058759117,0.014328968],"category_scores_gemma":[0.00175202,0.00007976115,0.000143321,0.00016170413,0.00026329988,0.0004785836,0.00010582998,0.00019631967,0.00024003624],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.009103719,0.0020851707,0.010440237,0.00004883081,0.0032653322,0.0014366581,0.001517035,0.000011014523,0.0033709577,0.7046016,0.23040588,0.03371357],"study_design_scores_gemma":[0.004264522,0.00034249036,0.0002888727,0.0007428769,0.0001295255,0.0035336483,0.001616848,0.000030183764,0.002896369,0.95561785,0.030194404,0.00034243043],"about_ca_topic_score_codex":0.0000030447595,"about_ca_topic_score_gemma":0.0000064588594,"teacher_disagreement_score":0.5592588,"about_ca_system_score_codex":0.0001991738,"about_ca_system_score_gemma":0.00021088768,"threshold_uncertainty_score":0.9865721},"labels":[],"label_agreement":null},{"id":"W2233031612","doi":"10.1142/s1793042117500014","title":"Central limit theorem for Artin L-functions","year":2016,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Central limit theorem; Congruence (geometry); Limit (mathematics); Gaussian; Infinity; Character (mathematics); Pure mathematics; Combinatorics; Mathematical analysis; Physics; Geometry; Quantum mechanics; Statistics","score_opus":0.06927443047457743,"score_gpt":0.38722058330035336,"score_spread":0.31794615282577593,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2233031612","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.035189725,0.00016946392,0.8692388,0.0065363706,0.011281968,0.0009387669,0.0030283208,0.00011846969,0.07349813],"genre_scores_gemma":[0.9209695,0.0001070267,0.015255225,0.00045560917,0.01027368,0.00011619184,0.00011795326,0.00024959457,0.052455254],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9960435,0.00052721886,0.0012853057,0.00035277705,0.0012734534,0.00051776425],"domain_scores_gemma":[0.98946995,0.006006624,0.0014933567,0.00052268355,0.0022406173,0.000266761],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0034385996,0.0003791375,0.0006500541,0.00032194902,0.000088610854,0.00018003551,0.001904853,0.00032809988,0.010819971],"category_scores_gemma":[0.005455778,0.00027669745,0.0010780896,0.00006750555,0.00029041583,0.00021118695,0.00067290897,0.0010106965,0.00018181022],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0017804572,0.00042150295,0.000556505,0.000090291935,0.0028863272,0.000109924214,0.00061365275,0.000026762153,0.00012015812,0.857099,0.12750997,0.008785455],"study_design_scores_gemma":[0.0011081259,0.000054712153,0.000072858486,0.0008098999,0.0002324931,0.00038405613,0.00034958989,0.00008420494,0.00039433906,0.9653766,0.030850878,0.00028221874],"about_ca_topic_score_codex":0.0000022195634,"about_ca_topic_score_gemma":0.0000040352775,"teacher_disagreement_score":0.88577974,"about_ca_system_score_codex":0.0005807481,"about_ca_system_score_gemma":0.00061593886,"threshold_uncertainty_score":0.9999685},"labels":[],"label_agreement":null},{"id":"W2239901248","doi":"10.1142/s179304211650127x","title":"Analogues of the binomial coefficient theorems of Gauss and Jacobi","year":2016,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Binomial coefficient; Congruence relation; Modulo; Gaussian binomial coefficient; Binomial theorem; Quotient; Central binomial coefficient; Pure mathematics; Catalan number; Gauss; Function (biology); Combinatorics; Negative binomial distribution; Statistics","score_opus":0.022599891892731094,"score_gpt":0.3226521901056482,"score_spread":0.3000522982129171,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2239901248","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9627541,0.00008322823,0.029492773,0.0004933658,0.0007006709,0.00009584628,0.00012584857,0.00000730068,0.0062469207],"genre_scores_gemma":[0.99664414,0.00003991733,0.002113116,0.000025261437,0.00012612599,0.000001146333,2.8618337e-7,0.000012456417,0.0010375512],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99862754,0.00012357945,0.0005976626,0.00006760792,0.0004955542,0.00008804194],"domain_scores_gemma":[0.9963624,0.002148762,0.00079554704,0.00015055882,0.00050643046,0.000036320067],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00073514023,0.00008998338,0.00024444563,0.000075352225,0.000018849772,0.000010882743,0.00046530235,0.000038548642,0.0007007954],"category_scores_gemma":[0.0015889431,0.0000442322,0.00015489526,0.000050593168,0.00047192225,0.00014262406,0.00014567471,0.00008406316,0.0000049163164],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00017683789,0.00017436486,0.0010955075,0.000035258614,0.00023495282,0.000006596794,0.0006648675,0.0000051850316,0.008798669,0.98598295,0.001181405,0.0016433718],"study_design_scores_gemma":[0.0005563927,0.000033687196,0.0008489867,0.0005011509,0.000043021555,0.00015253374,0.00035502814,0.000007620498,0.020599745,0.9765745,0.00027239378,0.000054948305],"about_ca_topic_score_codex":0.000001488438,"about_ca_topic_score_gemma":0.0000020433863,"teacher_disagreement_score":0.033890095,"about_ca_system_score_codex":0.00004649314,"about_ca_system_score_gemma":0.00004458792,"threshold_uncertainty_score":0.7673218},"labels":[],"label_agreement":null},{"id":"W2272437323","doi":"10.1142/s1793042117501147","title":"Orders of reductions of elliptic curves with many and few prime factors","year":2017,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"National Science Foundation","keywords":"Mathematics; Elliptic curve; Prime (order theory); Asymptotic formula; Sato–Tate conjecture; Supersingular elliptic curve; Function (biology); Pure mathematics; Combinatorics; Modular elliptic curve; Quarter period","score_opus":0.0308604881257617,"score_gpt":0.33040040556840095,"score_spread":0.29953991744263925,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2272437323","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.99096924,0.00017701866,0.0023502456,0.00037260418,0.00039410553,0.00006748943,0.000040088173,0.0000058405863,0.0056233536],"genre_scores_gemma":[0.99674726,0.00015699917,0.0019825133,0.000023520239,0.00010726678,9.4481726e-7,0.0000022896465,0.000015983067,0.00096322707],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9987965,0.000098145516,0.00047718192,0.000092921626,0.00043775202,0.000097459364],"domain_scores_gemma":[0.9971099,0.00067907,0.0013424216,0.00025508096,0.0005506724,0.00006286543],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00075500814,0.00012002844,0.00030578775,0.000116867915,0.00007180594,0.000025083336,0.00053419516,0.000049446957,0.0012560544],"category_scores_gemma":[0.0010650445,0.000087316796,0.00011459197,0.00004273917,0.0004546671,0.0003313721,0.000080156584,0.00018087913,0.000003365201],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.001426252,0.0009413423,0.05538298,0.0004610983,0.0035402493,0.00007169667,0.0030140837,0.00000946606,0.0023797643,0.9252245,0.003633198,0.003915387],"study_design_scores_gemma":[0.0014700878,0.000230457,0.032601096,0.002282329,0.00034709947,0.0010293582,0.0023057833,0.0000057330017,0.018951088,0.939563,0.0009689988,0.00024501592],"about_ca_topic_score_codex":0.0000108326485,"about_ca_topic_score_gemma":0.000001807529,"teacher_disagreement_score":0.022781882,"about_ca_system_score_codex":0.000022967775,"about_ca_system_score_gemma":0.00007003346,"threshold_uncertainty_score":0.9996569},"labels":[],"label_agreement":null},{"id":"W2277868817","doi":"10.1142/s179304211650130x","title":"On a restricted linear congruence","year":2016,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Ramanujan's sum; Mathematics; Sander; Congruence (geometry); Arithmetic function; Combinatorics; Discrete mathematics; Algebra over a field; Pure mathematics","score_opus":0.032357781786436966,"score_gpt":0.36474017339046405,"score_spread":0.3323823916040271,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2277868817","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.5976449,0.00004956775,0.30542362,0.0043149423,0.003651675,0.00024180596,0.00021928227,0.00014332449,0.08831086],"genre_scores_gemma":[0.95988643,0.000045850415,0.021634465,0.0002896869,0.0006221157,0.0000049869486,0.000001026141,0.000036463767,0.017479002],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99862564,0.00009349556,0.00046919112,0.00008572742,0.00060577755,0.00012016202],"domain_scores_gemma":[0.99418193,0.0045660767,0.00042931945,0.00014462182,0.00060682493,0.00007124965],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00036848508,0.000101695325,0.000179395,0.000104105224,0.000021157359,0.000022800948,0.00048797653,0.000044252145,0.0047079097],"category_scores_gemma":[0.0077785566,0.000060389706,0.00012140061,0.000051762676,0.00011373472,0.0002811083,0.00005712771,0.00013454785,0.00032418326],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00024607088,0.00014232464,0.000052531926,0.000006384811,0.00013903703,0.00015502665,0.000107605134,0.00000189706,0.0011089616,0.9838764,0.012405106,0.0017586417],"study_design_scores_gemma":[0.0006240368,0.000051040286,0.00007768117,0.00045981715,0.000016218188,0.0002992465,0.000057844914,0.000004490518,0.0021257694,0.99349725,0.0027068218,0.00007976446],"about_ca_topic_score_codex":5.305433e-7,"about_ca_topic_score_gemma":6.687603e-7,"teacher_disagreement_score":0.36224148,"about_ca_system_score_codex":0.000117812604,"about_ca_system_score_gemma":0.00004854326,"threshold_uncertainty_score":0.99620193},"labels":[],"label_agreement":null},{"id":"W2335096025","doi":"10.1142/s1793042117500142","title":"Fundamental units and consecutive squarefull numbers","year":2016,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Conjecture; Mathematics; Lonely runner conjecture; Collatz conjecture; abc conjecture; Elliott–Halberstam conjecture; Beal's conjecture; Combinatorics; Number theory","score_opus":0.030646398859440583,"score_gpt":0.31516740725478226,"score_spread":0.28452100839534167,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2335096025","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9727892,0.00007339011,0.004856094,0.0010564539,0.001192421,0.0000736531,0.00016641188,0.000027262897,0.019765107],"genre_scores_gemma":[0.9949457,0.000048384354,0.0010414341,0.00033568908,0.00037140716,0.0000023499476,0.000002657683,0.000023295303,0.00322906],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9984404,0.00026235252,0.00048656776,0.00013893368,0.0004910681,0.0001806849],"domain_scores_gemma":[0.995818,0.0028456615,0.00047223922,0.00012544337,0.00059790607,0.0001407173],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0010636913,0.00016280443,0.00024077971,0.00013417128,0.000051960214,0.000040554653,0.00039077539,0.00007930038,0.0079257125],"category_scores_gemma":[0.0015304937,0.00010665534,0.00010541581,0.000105598636,0.0003045866,0.0003630439,0.00011465263,0.00017641638,0.00012760561],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0012518348,0.00020297385,0.009278003,0.000014694772,0.0009997678,0.00031197647,0.0017084902,1.4304366e-7,0.0010799123,0.9480837,0.018893559,0.018174967],"study_design_scores_gemma":[0.0017297672,0.00008103205,0.0011321638,0.00029959888,0.0000554441,0.0027474968,0.0018496774,5.4517983e-7,0.0021043953,0.9712525,0.018565249,0.00018214947],"about_ca_topic_score_codex":0.0000022056627,"about_ca_topic_score_gemma":0.0000014822307,"teacher_disagreement_score":0.023168804,"about_ca_system_score_codex":0.00011644186,"about_ca_system_score_gemma":0.00008824653,"threshold_uncertainty_score":0.9929812},"labels":[],"label_agreement":null},{"id":"W2425961652","doi":"10.1142/s1793042117500907","title":"Mahler measures of polynomials that are sums of a bounded number of monomials","year":2016,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Northern British Columbia","funders":"","keywords":"Mathematics; Monomial; Polynomial; Logarithm; Integer (computer science); Combinatorics; Bounded function; Measure (data warehouse); Laurent polynomial; Discrete mathematics; Set (abstract data type); Mathematical analysis","score_opus":0.10161077380371702,"score_gpt":0.38299656632896645,"score_spread":0.2813857925252494,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2425961652","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9491454,0.00029470882,0.031240743,0.0004708646,0.0069015697,0.00057053886,0.0012615242,0.00003100252,0.010083673],"genre_scores_gemma":[0.97976005,0.000118094125,0.01817382,0.000024723615,0.00072454667,0.000013467662,0.0000059002814,0.00009695267,0.0010824214],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99468595,0.0004834043,0.002676156,0.0002575777,0.0016583826,0.00023855205],"domain_scores_gemma":[0.9826746,0.0037388257,0.010027073,0.00067857915,0.002768647,0.00011230426],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002344589,0.0004319254,0.0018046161,0.00028877234,0.0000202319,0.000032587937,0.0017877861,0.0004088133,0.0017558538],"category_scores_gemma":[0.0040344866,0.00033858966,0.0009265884,0.00007117817,0.00026823988,0.00023759178,0.0007180737,0.0005400224,0.000017544791],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.003525875,0.0018238454,0.010098223,0.0018446732,0.0085918205,0.0001001053,0.002889792,0.00006147084,0.012126336,0.944548,0.010580489,0.003809387],"study_design_scores_gemma":[0.0014053407,0.000035890604,0.00019402332,0.0042129126,0.00025707876,0.00016086297,0.00026416307,0.00000369353,0.056225665,0.93651664,0.0004648218,0.0002589064],"about_ca_topic_score_codex":0.00001362549,"about_ca_topic_score_gemma":0.000004030566,"teacher_disagreement_score":0.044099327,"about_ca_system_score_codex":0.0004504686,"about_ca_system_score_gemma":0.0004299565,"threshold_uncertainty_score":0.9999066},"labels":[],"label_agreement":null},{"id":"W2465890385","doi":"10.1142/s1793042117500154","title":"An infinite family of pairs of imaginary quadratic fields with ideal classes of a given order","year":2016,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"route_ca_aff":false,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"","funders":"Japan Society for the Promotion of Science; University of Lethbridge","keywords":"Mathematics; Ideal (ethics); The Imaginary; Quadratic equation; Order (exchange); Combinatorics; Pure mathematics; Discrete mathematics; Geometry; Law","score_opus":0.019145947623692757,"score_gpt":0.30898675111717117,"score_spread":0.2898408034934784,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2465890385","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.95709234,0.00006598228,0.034399472,0.00034628846,0.00025553175,0.00007396502,0.00009019043,0.000009360569,0.007666874],"genre_scores_gemma":[0.99219364,0.00003171986,0.007245025,0.00008181486,0.00012763821,0.0000020359523,0.0000026513142,0.000021681024,0.00029377503],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9978891,0.0003027041,0.00089523505,0.00011289779,0.0006667468,0.00013332344],"domain_scores_gemma":[0.9945933,0.002414418,0.0013006955,0.00024709085,0.0013715163,0.00007293428],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0011358293,0.00015442082,0.0004375869,0.00022225051,0.000016166854,0.000008531296,0.00060239434,0.00008448045,0.0019555714],"category_scores_gemma":[0.00075885747,0.000095993826,0.00016142962,0.0001631912,0.0003426104,0.00040735712,0.000060730177,0.00016731537,0.00000655562],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.010546082,0.0033285639,0.06966532,0.00053212175,0.0043223533,0.00032338992,0.007124352,0.00008599465,0.03697987,0.83485156,0.0066224616,0.025617952],"study_design_scores_gemma":[0.0019910375,0.0007910515,0.007225483,0.0011690219,0.00014080272,0.00044035885,0.001870255,0.000013963176,0.012220361,0.9735884,0.00036310373,0.00018613893],"about_ca_topic_score_codex":0.0000117711925,"about_ca_topic_score_gemma":0.0000039947336,"teacher_disagreement_score":0.13873689,"about_ca_system_score_codex":0.000031613232,"about_ca_system_score_gemma":0.00018315027,"threshold_uncertainty_score":0.9989568},"labels":[],"label_agreement":null},{"id":"W2477857434","doi":"10.1142/s179304211750083x","title":"Almost prime solutions to diophantine systems of high rank","year":2016,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Diophantine equation; Mathematics; Integer (computer science); Rank (graph theory); Combinatorics; Prime (order theory); Degree (music); Bounded function; Prime number; Physics; Mathematical analysis; Computer science","score_opus":0.03209395312103707,"score_gpt":0.3189606931654143,"score_spread":0.28686674004437723,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2477857434","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.62957215,0.0009989089,0.31525233,0.0023793157,0.024581565,0.00091836543,0.0030352336,0.0001089124,0.023153197],"genre_scores_gemma":[0.99090254,0.00005422451,0.0029701896,0.00013575148,0.0023639693,0.00001975467,0.000024538716,0.000068798276,0.0034602038],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9958465,0.00056314154,0.0017082837,0.00030037586,0.0012509826,0.00033071192],"domain_scores_gemma":[0.99262184,0.0023442332,0.0022920114,0.0005626065,0.0019677773,0.00021151178],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0032382512,0.00037645985,0.000945998,0.00048389848,0.000058486632,0.00007090842,0.001759928,0.00031649825,0.0034339738],"category_scores_gemma":[0.0024962786,0.00028884047,0.0005626928,0.00014129707,0.00017379796,0.00018643067,0.0010058407,0.0006706488,0.0001985211],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0014870125,0.0006563029,0.0004220026,0.00024807715,0.003447074,0.00018939172,0.0008513894,0.0001267135,0.0012823858,0.96549386,0.02321848,0.0025772902],"study_design_scores_gemma":[0.0011043214,0.000072518626,0.00039840327,0.0031740018,0.0002452105,0.0008997565,0.00023045288,0.0000073750534,0.002556009,0.9855312,0.0054235924,0.00035713174],"about_ca_topic_score_codex":0.000020490794,"about_ca_topic_score_gemma":0.0000012519005,"teacher_disagreement_score":0.3613304,"about_ca_system_score_codex":0.00023816238,"about_ca_system_score_gemma":0.0003043793,"threshold_uncertainty_score":0.99995637},"labels":[],"label_agreement":null},{"id":"W2549980981","doi":"10.1142/s1793042117500592","title":"Infinite products with coefficients which vanish on certain arithmetic progressions","year":2016,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Integer (computer science); Type (biology); Combinatorics; Variable (mathematics); Arithmetic progression; Arithmetic; Discrete mathematics; Mathematical analysis; Computer science","score_opus":0.030450400394248615,"score_gpt":0.34283317364211635,"score_spread":0.31238277324786773,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2549980981","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7199695,0.00007593868,0.18815409,0.014162976,0.0035831588,0.0010481558,0.00031013845,0.00025587346,0.072440185],"genre_scores_gemma":[0.9720283,0.0000138253,0.019978387,0.00011517947,0.0003630291,0.0000135585115,0.0000021458538,0.000045655128,0.007439897],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9979967,0.00014080532,0.00051892374,0.00016169104,0.0009807361,0.00020115469],"domain_scores_gemma":[0.995469,0.0021461004,0.0005655631,0.00022674615,0.0014939717,0.00009864924],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0006583682,0.0001702939,0.00025136926,0.00015388751,0.000051713756,0.000064097825,0.00052304845,0.00005098691,0.0013319446],"category_scores_gemma":[0.0052157887,0.000091429654,0.000072328476,0.00015133168,0.00015132649,0.00032055523,0.0000829245,0.0002039191,0.00012499298],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0011767227,0.001807463,0.000695815,0.000083518375,0.00073009374,0.00032313063,0.0010808302,0.000027335765,0.001800656,0.96826446,0.014889135,0.009120849],"study_design_scores_gemma":[0.0012732319,0.00020899448,0.0002041809,0.002019103,0.000056904482,0.0006262253,0.00025233353,0.000006970032,0.004085964,0.9848589,0.0062191184,0.00018809803],"about_ca_topic_score_codex":3.164965e-7,"about_ca_topic_score_gemma":0.0000026143377,"teacher_disagreement_score":0.25205883,"about_ca_system_score_codex":0.0001321772,"about_ca_system_score_gemma":0.00011296615,"threshold_uncertainty_score":0.999581},"labels":[],"label_agreement":null},{"id":"W2551783230","doi":"10.1142/s1793042118501099","title":"D-finite numbers","year":2018,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"semigroups and automata theory","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Class (philosophy); Algebraic number; Polynomial; Field (mathematics); Point (geometry); Constant (computer programming); Algebraic number field; Differential (mechanical device); Real number","score_opus":0.010393281732494403,"score_gpt":0.2805275340452899,"score_spread":0.27013425231279553,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2551783230","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.036993198,0.000078637546,0.86716056,0.001991722,0.0074810777,0.000042933534,0.000020199153,0.00009234257,0.08613931],"genre_scores_gemma":[0.9758934,0.000016065906,0.019468114,0.0020235467,0.0015463678,9.618014e-7,0.000001757477,0.000010759996,0.0010390325],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99870133,0.00012395777,0.00036747937,0.00013003315,0.00052489596,0.00015229749],"domain_scores_gemma":[0.998242,0.00048151947,0.0003421968,0.00022773253,0.00061644113,0.000090112364],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0009175725,0.0001002706,0.00012918629,0.00012289578,0.000048198748,0.00016195189,0.0019406448,0.000042591837,0.0028860974],"category_scores_gemma":[0.00026932042,0.00008182613,0.00013976997,0.00013386979,0.00013222286,0.0007609762,0.00021209712,0.00015361654,0.0007338178],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000114331335,0.00012529058,0.0007778405,0.0000018489659,0.00025924796,0.00025717393,0.0013887996,0.000014188268,0.0006221747,0.8674732,0.029105842,0.099860094],"study_design_scores_gemma":[0.00087386346,0.00012737785,0.0014522689,0.00012777802,0.000013506406,0.0020175448,0.00018586924,0.0022317155,0.0042735073,0.8040722,0.18438159,0.00024279187],"about_ca_topic_score_codex":0.0000030397953,"about_ca_topic_score_gemma":9.045913e-7,"teacher_disagreement_score":0.9389002,"about_ca_system_score_codex":0.000056534183,"about_ca_system_score_gemma":0.000077583485,"threshold_uncertainty_score":0.9980254},"labels":[],"label_agreement":null},{"id":"W2559798569","doi":"10.1142/s1793042117500816","title":"On the quadratic divisor problem","year":2016,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Divisor (algebraic geometry); Divisor function; Quadratic equation; Pure mathematics; Zero divisor; Algebra over a field; Combinatorics; Geometry","score_opus":0.05024092634913191,"score_gpt":0.3633076727520708,"score_spread":0.3130667464029389,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2559798569","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.5862712,0.000056492216,0.106154814,0.050637513,0.0020727734,0.00062534807,0.00016625269,0.00009434606,0.25392124],"genre_scores_gemma":[0.98233086,0.000014300479,0.0011514854,0.0005334664,0.00046566213,0.000009491776,5.8162544e-7,0.000032212578,0.015461941],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9974654,0.0005312878,0.0005428611,0.00012106963,0.0011295408,0.00020984527],"domain_scores_gemma":[0.9882277,0.010344456,0.0004464249,0.0002704204,0.00061965006,0.000091346796],"candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0029980906,0.00014048247,0.00020280592,0.00010986418,0.00006228873,0.0000662853,0.0011659993,0.000049740756,0.021280123],"category_scores_gemma":[0.004218881,0.000062003695,0.00022559166,0.00008611562,0.00020731094,0.0001965174,0.00011757899,0.00026983584,0.0009281369],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0003220197,0.00017092857,0.00031028892,0.0000047207413,0.00040601802,0.00007254083,0.00027053108,7.33643e-7,0.0003240409,0.9413627,0.050627287,0.0061282185],"study_design_scores_gemma":[0.0005737038,0.00006533806,0.00009386418,0.00032936706,0.000025722757,0.00029455504,0.00018802621,0.0000070281035,0.0006394758,0.99188817,0.0058046402,0.00009013471],"about_ca_topic_score_codex":0.0000011337214,"about_ca_topic_score_gemma":0.0000018021872,"teacher_disagreement_score":0.39605963,"about_ca_system_score_codex":0.00016576672,"about_ca_system_score_gemma":0.0001059667,"threshold_uncertainty_score":0.99984974},"labels":[],"label_agreement":null},{"id":"W2560125711","doi":"10.1142/s1793042117500865","title":"A variant of Heilbronn characters","year":2016,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Quotient; Mathematics; Conjecture; Formalism (music); Simple (philosophy); Elliptic curve; Pure mathematics; Arithmetic; Algebra over a field; Literature","score_opus":0.020189958918135378,"score_gpt":0.3288314882358674,"score_spread":0.30864152931773203,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2560125711","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8873685,0.00005258313,0.1026331,0.0015006409,0.0016709934,0.000057650235,0.00010473127,0.000016316182,0.0065955115],"genre_scores_gemma":[0.99454546,0.00003429084,0.003556423,0.00012978486,0.00040964826,9.4342244e-7,8.739811e-7,0.000013866789,0.0013087188],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9989021,0.00006784294,0.00046167255,0.00006718013,0.0004034302,0.00009779448],"domain_scores_gemma":[0.99764746,0.001154892,0.00060885114,0.00011191791,0.00042246093,0.000054393873],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00051533955,0.000081621874,0.00018659423,0.0001140346,0.000011182269,0.000008058569,0.00037835675,0.00003843552,0.003363802],"category_scores_gemma":[0.0010208135,0.00004896047,0.00015488618,0.00005241011,0.00006857662,0.00025247704,0.000049354698,0.00008894881,0.00005354406],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00045347132,0.00025624663,0.0012021834,0.000013277164,0.0005474494,0.00018529446,0.0003559376,8.743857e-7,0.007016467,0.94851387,0.0027863581,0.038668603],"study_design_scores_gemma":[0.0007967892,0.000039120947,0.0015204757,0.0002844214,0.000023357705,0.0006797919,0.00009644535,7.713793e-7,0.004059645,0.9889826,0.0034414942,0.00007508876],"about_ca_topic_score_codex":2.324267e-7,"about_ca_topic_score_gemma":2.8469805e-7,"teacher_disagreement_score":0.107176974,"about_ca_system_score_codex":0.000053656266,"about_ca_system_score_gemma":0.000046004498,"threshold_uncertainty_score":0.99754727},"labels":[],"label_agreement":null},{"id":"W2583321877","doi":"10.1142/s1793042117500956","title":"Patterns of primes in Chebotarev sets","year":2017,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Generalization; Prime (order theory); Set (abstract data type); Discrete mathematics; Combinatorics; Pure mathematics; Mathematical analysis; Computer science","score_opus":0.060850700407411855,"score_gpt":0.4148828366032325,"score_spread":0.35403213619582063,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2583321877","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.97732717,0.00002696568,0.0013431623,0.0006535228,0.00046618373,0.00007742527,0.00006454122,0.000005670617,0.020035356],"genre_scores_gemma":[0.99607086,0.000028848146,0.0015229734,0.00005284411,0.00021259389,0.000002040722,0.0000020391522,0.000021538339,0.002086236],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99801475,0.00017594092,0.000678113,0.0001109104,0.0008488552,0.00017141365],"domain_scores_gemma":[0.99682677,0.0010892597,0.0010150052,0.00038988257,0.0006031825,0.000075912874],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0024554355,0.00011742983,0.0003262731,0.00016764505,0.000041336978,0.00007490245,0.0017248447,0.00006574941,0.004777279],"category_scores_gemma":[0.0029828427,0.00009740852,0.00019445452,0.00002829637,0.000115248484,0.0003265211,0.00026585278,0.00032342755,0.0000448769],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0010514099,0.00079797715,0.4776798,0.00009760673,0.0010359838,0.00084146817,0.001962036,0.000006831583,0.0010051726,0.4945645,0.0056031058,0.015354111],"study_design_scores_gemma":[0.0012891011,0.00003841677,0.042094313,0.0005906473,0.000031076295,0.0003544966,0.00049201044,0.00003117146,0.0033313362,0.9505392,0.001082942,0.00012529746],"about_ca_topic_score_codex":0.000034227804,"about_ca_topic_score_gemma":0.000029789757,"teacher_disagreement_score":0.4559747,"about_ca_system_score_codex":0.00012090485,"about_ca_system_score_gemma":0.00013521177,"threshold_uncertainty_score":0.9961325},"labels":[],"label_agreement":null},{"id":"W2593262293","doi":"10.1142/s1793042117501196","title":"The Mahler measure of a Weierstrass form","year":2017,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Identity (music); Measure (data warehouse); Pure mathematics; Elliptic curve; Elliptic function; Torsion (gastropod); Rational function; Algebra over a field; Mathematical analysis","score_opus":0.03544189859508277,"score_gpt":0.3412493864608544,"score_spread":0.3058074878657716,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2593262293","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7995474,0.00030153795,0.012290012,0.0067435675,0.006367249,0.00022580956,0.00011345544,0.00002895858,0.17438206],"genre_scores_gemma":[0.9938472,0.000042007527,0.0010446822,0.00006958027,0.00055727275,0.000002111169,9.257974e-7,0.000018229193,0.0044180183],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9982676,0.0001419809,0.0005802878,0.00008376762,0.00076473167,0.00016162236],"domain_scores_gemma":[0.99558663,0.0016967283,0.0014265773,0.0004126076,0.0008064756,0.00007099005],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0028750875,0.00012369412,0.00022879637,0.000059982784,0.00024058663,0.00011674108,0.0017235499,0.00007613457,0.0015036106],"category_scores_gemma":[0.0034631416,0.000078245896,0.0002899873,0.000030341891,0.00023250084,0.0003525193,0.00015002317,0.00029752633,0.00003941199],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0009706437,0.00019107018,0.0026205124,0.000018244324,0.0012293885,0.00007963852,0.00086972216,9.128842e-7,0.00031076276,0.9464515,0.017134067,0.03012355],"study_design_scores_gemma":[0.000685935,0.000033646364,0.0023245052,0.00016317228,0.000055548204,0.00045400832,0.00053502596,0.000003870886,0.0017226975,0.98141026,0.012522635,0.00008866139],"about_ca_topic_score_codex":0.0000041478775,"about_ca_topic_score_gemma":0.0000060147236,"teacher_disagreement_score":0.19429983,"about_ca_system_score_codex":0.00009530262,"about_ca_system_score_gemma":0.000089804555,"threshold_uncertainty_score":0.99940914},"labels":[],"label_agreement":null},{"id":"W2605338013","doi":"10.1142/s1793042117501275","title":"The analog of the Erdös distance problem in finite fields","year":2017,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Finite field; Mathematics; Kloosterman sum; Prime (order theory); Vector space; Field (mathematics); Pure mathematics; Discrete mathematics; Algebra over a field; Combinatorics","score_opus":0.020386345617964152,"score_gpt":0.3301244443810287,"score_spread":0.3097380987630646,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2605338013","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.82587296,0.00038249194,0.006444909,0.0063289916,0.0056336285,0.00029830998,0.0001085814,0.000011342414,0.1549188],"genre_scores_gemma":[0.9976487,0.000060550454,0.0006490026,0.0001158944,0.00021259203,0.0000020294653,2.816428e-7,0.000008613725,0.0013023138],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99876446,0.00016864807,0.00047606585,0.000065939654,0.00041723537,0.00010766011],"domain_scores_gemma":[0.9966531,0.0016932801,0.00096037256,0.00039388228,0.00027594066,0.000023446655],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0012780608,0.00008488251,0.00015111845,0.000035237394,0.00023897002,0.00007220849,0.0018068838,0.000054770837,0.00022364264],"category_scores_gemma":[0.0019084088,0.000041831878,0.00018950665,0.000032434564,0.00032363334,0.00014336087,0.000232901,0.00032480096,0.0000013536165],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00021825731,0.000042644482,0.014711172,0.000008816623,0.00014666578,0.000018446859,0.00094538846,0.000025462328,0.000015920183,0.97638804,0.002267076,0.0052121035],"study_design_scores_gemma":[0.00035859237,0.000012545737,0.014381935,0.00018158846,0.000014200487,0.000057461584,0.00014816562,0.000028980068,0.0001961454,0.9788515,0.0057186475,0.000050258917],"about_ca_topic_score_codex":0.00000739332,"about_ca_topic_score_gemma":0.00006530413,"teacher_disagreement_score":0.17177579,"about_ca_system_score_codex":0.000032906446,"about_ca_system_score_gemma":0.00004644681,"threshold_uncertainty_score":0.33576697},"labels":[],"label_agreement":null},{"id":"W2754703134","doi":"10.1142/s1793042118500422","title":"Families of even non-congruent numbers with prime factors in each odd congruence class modulo eight","year":2017,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Okanagan University College; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Congruence (geometry); Modulo; Congruence relation; Prime k-tuple; Prime (order theory); Combinatorics; Class (philosophy); Prime number; Arithmetic; Prime factor; Discrete mathematics; Computer science","score_opus":0.03356306622623563,"score_gpt":0.35793519874396973,"score_spread":0.3243721325177341,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2754703134","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9706814,0.000016971162,0.0022401968,0.0003297976,0.0004761076,0.00018272096,0.000084053776,0.00000862871,0.02598011],"genre_scores_gemma":[0.99515796,0.000034105105,0.0017294124,0.000037640017,0.00016970684,0.0000057298785,0.00000678635,0.00004386871,0.0028148105],"study_design_codex":"observational","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99678135,0.0002636679,0.000934612,0.00024083661,0.0014410373,0.00033847758],"domain_scores_gemma":[0.9951604,0.0014467322,0.0014811298,0.0006033983,0.001145375,0.00016296013],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0019698355,0.0002673284,0.00060822506,0.00029098848,0.00009718638,0.00012722494,0.0021026456,0.000121220524,0.0015694265],"category_scores_gemma":[0.0017949489,0.00019739073,0.0002347141,0.00009447592,0.0006510775,0.0007088164,0.00026100548,0.0005955061,0.00003562136],"study_design_candidate":"observational","study_design_consensus":null,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0024593496,0.0012250731,0.7996406,0.00012398486,0.0025108242,0.000924065,0.006413136,0.00010938927,0.0024091906,0.17823918,0.003376446,0.0025687565],"study_design_scores_gemma":[0.007256261,0.00036481547,0.19593179,0.0026128,0.00024424808,0.0009962672,0.008080865,0.0006095817,0.022431701,0.75789034,0.0026514132,0.00092988653],"about_ca_topic_score_codex":0.00025837295,"about_ca_topic_score_gemma":0.00020674062,"teacher_disagreement_score":0.6037088,"about_ca_system_score_codex":0.00032202905,"about_ca_system_score_gemma":0.0003524276,"threshold_uncertainty_score":0.9993433},"labels":[],"label_agreement":null},{"id":"W2755009224","doi":"10.1142/s1793042118500537","title":"Applications of group theory to conjectures of Artin and Langlands","year":2017,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Langlands program; Mathematics; Artin L-function; Langlands dual group; Automorphic L-function; Pure mathematics; Group (periodic table); Algebra over a field; Automorphic form; Conjecture; Conductor; Geometry","score_opus":0.015682266246749715,"score_gpt":0.35961426769478466,"score_spread":0.34393200144803493,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2755009224","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8129565,0.00013761989,0.17620471,0.0003993606,0.00027351463,0.000121106204,0.0001330721,0.0000073905794,0.009766688],"genre_scores_gemma":[0.9927435,0.000015744386,0.0065848944,0.00008084991,0.00019952715,0.0000036986837,0.0000020230343,0.000009170454,0.00036060394],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9992344,0.00004997861,0.00034363015,0.00006435799,0.0002437292,0.00006390911],"domain_scores_gemma":[0.99791527,0.0008439242,0.00068626244,0.00018560847,0.00031837882,0.000050531395],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006404694,0.00006802258,0.00018829801,0.00010030237,0.000038037448,0.00001878493,0.00042226605,0.000035032655,0.00046271077],"category_scores_gemma":[0.0010017245,0.00005225499,0.000076072676,0.000028210487,0.000120450524,0.00011303592,0.00009336791,0.00009501623,0.0000048343863],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0003052334,0.00012923997,0.006357577,0.000027536018,0.00023173075,0.000008654779,0.0005485628,0.0000035858245,0.0015807806,0.95345825,0.00083292474,0.0365159],"study_design_scores_gemma":[0.00043647963,0.00004309024,0.007509441,0.000100956226,0.000029884923,0.00009369007,0.00027578534,0.000001645951,0.0031561065,0.9842786,0.0040192483,0.00005504223],"about_ca_topic_score_codex":0.0000010173927,"about_ca_topic_score_gemma":0.00000281755,"teacher_disagreement_score":0.17978695,"about_ca_system_score_codex":0.000011959642,"about_ca_system_score_gemma":0.000016919601,"threshold_uncertainty_score":0.50663584},"labels":[],"label_agreement":null},{"id":"W2756299746","doi":"10.1142/s1793042118500446","title":"A unifying look at zero-sum invariants","year":2017,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Brock University","funders":"Natural Sciences and Engineering Research Council of Canada; Science and Technology Development Fund; National Science Foundation","keywords":"Mathematics; Zero (linguistics); Subsequence; Combinatorics; Integer (computer science); Abelian group; Sequence (biology); Discrete mathematics; Computer science","score_opus":0.049688844139663034,"score_gpt":0.335747157454206,"score_spread":0.286058313314543,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2756299746","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.92329085,0.00006068867,0.0059058648,0.0010423491,0.002659983,0.000069448324,0.00003657636,0.000022788683,0.06691148],"genre_scores_gemma":[0.9871196,0.000044310393,0.0037349134,0.0002792995,0.0009346948,0.0000015863718,0.0000025577588,0.00002909141,0.007853914],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9985848,0.00008621844,0.00047168904,0.00012307327,0.0005665826,0.00016763751],"domain_scores_gemma":[0.99771863,0.00046753424,0.0009992513,0.00032760671,0.00038750033,0.00009950107],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00097368675,0.00013455357,0.00022728709,0.00008699943,0.00020426535,0.00021307847,0.0011685174,0.00006774478,0.003202765],"category_scores_gemma":[0.0016073982,0.00011203658,0.00018865187,0.000015410018,0.00013117479,0.0005356089,0.00028312148,0.00024232375,0.00026312403],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0006071707,0.00037165204,0.019424707,0.000038604558,0.0010989204,0.0010621304,0.0016713823,0.0000066579205,0.002111331,0.8995178,0.061125223,0.01296447],"study_design_scores_gemma":[0.00097496714,0.000021864687,0.005441388,0.00032407822,0.00004239483,0.0011060683,0.0001124388,0.000019168638,0.0018375032,0.97661614,0.013352387,0.00015157803],"about_ca_topic_score_codex":0.0000076208216,"about_ca_topic_score_gemma":0.000009620404,"teacher_disagreement_score":0.077098414,"about_ca_system_score_codex":0.00015129313,"about_ca_system_score_gemma":0.00006976498,"threshold_uncertainty_score":0.99770844},"labels":[],"label_agreement":null},{"id":"W2766846018","doi":"10.1142/s1793042118500653","title":"On the equation Resx(P(x),x2 + sx + t) = a","year":2017,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université Laval","funders":"","keywords":"Mathematics; Diophantine equation; Diophantine set; Thue equation; Pure mathematics; Diophantine geometry; Algebra over a field; Discrete mathematics","score_opus":0.06792433455319753,"score_gpt":0.3588082899562015,"score_spread":0.290883955403004,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2766846018","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.80090714,0.00003077473,0.012471922,0.009347036,0.0030048294,0.0001634201,0.000048395174,0.00003099069,0.17399551],"genre_scores_gemma":[0.99358475,0.000011294669,0.00069070177,0.0007537186,0.0009187376,0.0000046336013,0.0000023585094,0.00002172548,0.0040120888],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99815863,0.00029916756,0.00048345883,0.000116172436,0.0007890898,0.00015349383],"domain_scores_gemma":[0.9938718,0.0039061655,0.0011658532,0.0005081519,0.0004815364,0.00006650585],"candidate_categories":["metaresearch","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0031457297,0.00014086577,0.00018694553,0.00009085373,0.00029518615,0.0002188726,0.0016237631,0.00007466492,0.008209062],"category_scores_gemma":[0.009769037,0.00008882372,0.0002273183,0.000035665664,0.00019400773,0.0003622851,0.00014401002,0.00039552673,0.000380145],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00046622104,0.00013754122,0.0002855455,0.0000040536715,0.00029105926,0.000072912095,0.00046230023,0.0000034626046,0.00007034281,0.9695746,0.02405473,0.004577269],"study_design_scores_gemma":[0.0005315284,0.0000478861,0.0011282491,0.00021027953,0.00003118092,0.0002726257,0.00029615464,0.00001994006,0.00100022,0.99095666,0.005404581,0.00010070703],"about_ca_topic_score_codex":0.000002945618,"about_ca_topic_score_gemma":0.0000013934352,"teacher_disagreement_score":0.19267762,"about_ca_system_score_codex":0.00008609955,"about_ca_system_score_gemma":0.000062860185,"threshold_uncertainty_score":0.9985721},"labels":[],"label_agreement":null},{"id":"W2788702337","doi":"10.1142/s1793042118501646","title":"Perfect powers that are sums of squares in a three term arithmetic progression","year":2018,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Factorization; Term (time); Mathematics; Arithmetic; Argument (complex analysis); Arithmetic progression; Discrete mathematics; Algebra over a field; Pure mathematics; Algorithm","score_opus":0.040234667890617984,"score_gpt":0.35584353145358993,"score_spread":0.31560886356297196,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2788702337","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9866632,0.00044093447,0.0024636413,0.00037468993,0.0031695303,0.00031385774,0.00016650917,0.000028174089,0.006379443],"genre_scores_gemma":[0.9954416,0.00007592413,0.0032966253,0.000066184286,0.00076353416,0.000016198188,0.00002123042,0.00006375706,0.0002549145],"study_design_codex":"observational","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99627507,0.0005642706,0.0011418201,0.0003413623,0.0013809828,0.00029649257],"domain_scores_gemma":[0.9937486,0.001865621,0.002864007,0.00048062604,0.0009209411,0.00012019534],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0032481425,0.00041578885,0.00088477944,0.00065383554,0.000037293754,0.000082051454,0.0016112112,0.000415397,0.0034954976],"category_scores_gemma":[0.0018132564,0.000335784,0.00060689496,0.00015029301,0.00038819513,0.00022523646,0.0007702577,0.0012133264,0.000038646118],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.012094325,0.005163239,0.5899401,0.0029663262,0.007966907,0.0034721189,0.013083865,0.00008410764,0.0009294306,0.3035416,0.01785458,0.042903442],"study_design_scores_gemma":[0.0011779774,0.00013879834,0.01737339,0.0064919526,0.00014698174,0.0006051598,0.0009449877,0.000022418668,0.002688342,0.96966845,0.00038721494,0.0003543548],"about_ca_topic_score_codex":0.0000066512844,"about_ca_topic_score_gemma":0.000018996765,"teacher_disagreement_score":0.66612685,"about_ca_system_score_codex":0.00025897307,"about_ca_system_score_gemma":0.00023331706,"threshold_uncertainty_score":0.9999094},"labels":[],"label_agreement":null},{"id":"W2799241853","doi":"10.1142/s1793042118501397","title":"Simultaneous non-vanishing and sign changes of Fourier coefficients of modular forms","year":2018,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Sign (mathematics); Fourier series; Modular design; Mathematics; Fourier transform; Modular form; Pure mathematics; Arithmetic; Mathematical analysis; Computer science","score_opus":0.03683057540356189,"score_gpt":0.36259756833763723,"score_spread":0.32576699293407535,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2799241853","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9194499,0.0001292827,0.07195045,0.0002065391,0.0010065979,0.00033253393,0.00042515685,0.000013031466,0.006486465],"genre_scores_gemma":[0.9897904,0.000103272534,0.008277122,0.00004406571,0.00053910486,0.000004241043,0.000014389101,0.00006264948,0.0011647675],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9964149,0.00028297573,0.0011109011,0.00026224292,0.0016712847,0.00025770592],"domain_scores_gemma":[0.9915644,0.0031767774,0.002088539,0.00041452536,0.0026127421,0.00014304735],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.003359806,0.0002953886,0.0008124658,0.00034977635,0.000037819398,0.00006559266,0.0013806612,0.0002734062,0.0016286743],"category_scores_gemma":[0.0036537522,0.00024191194,0.00030668115,0.0000913504,0.00050557347,0.00013125941,0.0010367396,0.00071843143,0.000013089964],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.021657703,0.0103603555,0.012699431,0.009803453,0.048089802,0.004845634,0.06032497,0.010973123,0.0231422,0.5981384,0.028678177,0.17128676],"study_design_scores_gemma":[0.0011082116,0.00022401822,0.000087039996,0.0022680585,0.00025879132,0.00038817254,0.0008776374,0.00565474,0.00614666,0.9820244,0.0006703677,0.0002919056],"about_ca_topic_score_codex":0.000013276435,"about_ca_topic_score_gemma":0.0000063650937,"teacher_disagreement_score":0.383886,"about_ca_system_score_codex":0.00015191804,"about_ca_system_score_gemma":0.00022732338,"threshold_uncertainty_score":0.99928397},"labels":[],"label_agreement":null},{"id":"W2803119001","doi":"10.1142/s1793042118501427","title":"Number fields with large minimal index containing quadratic subfields","year":2018,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Discriminant; Quadratic equation; Index (typography); Algebraic number field; Combinatorics; Field (mathematics); Upper and lower bounds; Discrete mathematics; Pure mathematics; Mathematical analysis; Geometry; Artificial intelligence; Computer science","score_opus":0.03462076985626999,"score_gpt":0.3724898614287926,"score_spread":0.3378690915725226,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2803119001","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7548488,0.000017660113,0.11653597,0.001140936,0.0009536529,0.00015748625,0.0000422751,0.000046297115,0.12625693],"genre_scores_gemma":[0.9887125,0.000005219154,0.0037672275,0.0005982994,0.0015236031,0.000005359675,0.000004361449,0.000045000146,0.005338413],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.997151,0.00034399008,0.0007131799,0.00019976939,0.0012022782,0.00038976505],"domain_scores_gemma":[0.9954698,0.0020494955,0.00056376343,0.00028288495,0.0014542607,0.00017980157],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0022870474,0.00021989986,0.00038601912,0.00014611421,0.000104330495,0.000122779,0.0009215804,0.00015804432,0.02974705],"category_scores_gemma":[0.0012239979,0.00016504075,0.00019421063,0.00015232692,0.00029265572,0.00038807155,0.00016321163,0.0006329297,0.0004203379],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.006636029,0.00080674514,0.09334118,0.000044175853,0.0025025778,0.0013038731,0.0058694175,0.000004049724,0.00007456137,0.8444912,0.041650046,0.00327618],"study_design_scores_gemma":[0.003982837,0.0006513851,0.0019918939,0.00054513605,0.00015325124,0.004067478,0.0049426663,0.0004364253,0.000758516,0.96685565,0.015150676,0.000464085],"about_ca_topic_score_codex":0.0000115163875,"about_ca_topic_score_gemma":0.00006626755,"teacher_disagreement_score":0.23386371,"about_ca_system_score_codex":0.00013261392,"about_ca_system_score_gemma":0.00024675945,"threshold_uncertainty_score":0.9711399},"labels":[],"label_agreement":null},{"id":"W2884781336","doi":"10.1142/s1793042118501750","title":"Indices in a number field II","year":2018,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Brock University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Cardinality (data modeling); Combinatorics; Order (exchange); Field (mathematics); Degree (music); Prime (order theory); Discrete mathematics; Pure mathematics; Physics","score_opus":0.021648606401848576,"score_gpt":0.3438962794384103,"score_spread":0.3222476730365617,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2884781336","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8977228,0.000023419925,0.0018312521,0.00080954336,0.0016873912,0.000054079694,0.000014015367,0.000018990047,0.09783853],"genre_scores_gemma":[0.99179214,0.000013096248,0.0027993354,0.00095870293,0.001446772,0.000002922829,0.0000021502947,0.000020408554,0.002964444],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9982564,0.00020619022,0.00064426864,0.00013336426,0.0005565229,0.00020325732],"domain_scores_gemma":[0.9971682,0.0016484426,0.00049353635,0.00016587564,0.00044126328,0.00008268026],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0016449842,0.00014724991,0.00025561437,0.00019271558,0.000063992135,0.000038791874,0.0007382684,0.00011745761,0.032817446],"category_scores_gemma":[0.0018002708,0.00012413277,0.000161414,0.0001908912,0.00013786713,0.00036361715,0.00017057876,0.00037309626,0.00039396583],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0018581518,0.00093138055,0.032947432,0.000024396631,0.0007066947,0.0004963023,0.0073894965,9.715509e-7,0.0002425129,0.8714166,0.062344287,0.02164177],"study_design_scores_gemma":[0.00088065147,0.00011648905,0.0014129533,0.00021453018,0.000023852252,0.0009980168,0.0006678458,0.000004138687,0.0026922242,0.9714533,0.021386549,0.00014944506],"about_ca_topic_score_codex":0.000007997525,"about_ca_topic_score_gemma":0.000011961001,"teacher_disagreement_score":0.1000367,"about_ca_system_score_codex":0.000079387086,"about_ca_system_score_gemma":0.000073398456,"threshold_uncertainty_score":0.9680667},"labels":[],"label_agreement":null},{"id":"W2895716569","doi":"10.1142/s1793042122500087","title":"Deformations of reducible Galois representations to Hida-families","year":2021,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Galois module; Mathematics; Modulo; Bar (unit); Congruence (geometry); Pure mathematics; Galois theory; Galois group; Combinatorics; Physics; Geometry","score_opus":0.03788215935751789,"score_gpt":0.3616770569789248,"score_spread":0.32379489762140695,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2895716569","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.89416194,0.00024012996,0.049636714,0.0015875956,0.005181036,0.00032647912,0.00062901934,0.00004888699,0.048188183],"genre_scores_gemma":[0.96514887,0.00014745028,0.031168895,0.00025359855,0.0007758876,0.000025212837,0.000119384975,0.00005016142,0.0023105459],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99636275,0.00044086666,0.0016076022,0.00027310627,0.0011022474,0.00021340731],"domain_scores_gemma":[0.9931301,0.0019012276,0.0016522293,0.00062629045,0.0025195002,0.00017063749],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0018219277,0.0002867651,0.00065772637,0.0006209059,0.00006538577,0.00012348851,0.0013201152,0.00022965496,0.0073675285],"category_scores_gemma":[0.004310584,0.00027085425,0.00063768827,0.00030841993,0.00014130547,0.0003644751,0.00085247075,0.00077841105,0.00006691245],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0015620124,0.0028985064,0.004872029,0.0008864988,0.009658694,0.00054780865,0.046371303,0.0038776014,0.002306795,0.7949325,0.11680333,0.015282904],"study_design_scores_gemma":[0.00053639954,0.00004298794,0.0010223716,0.0013928297,0.00026071267,0.0007777851,0.009732459,0.000018431627,0.008333301,0.97497064,0.002591467,0.00032058975],"about_ca_topic_score_codex":0.000029756107,"about_ca_topic_score_gemma":0.000009249386,"teacher_disagreement_score":0.18003815,"about_ca_system_score_codex":0.00020653158,"about_ca_system_score_gemma":0.0004895081,"threshold_uncertainty_score":0.99997437},"labels":[],"label_agreement":null},{"id":"W2897200622","doi":"10.1142/s1793042120500578","title":"Constructions of vector-valued modular forms of rank four and level one","year":2019,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Saskatchewan","funders":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada; Simons Foundation","keywords":"Rank (graph theory); Modular form; Mathematics; Isomorphism (crystallography); Modular design; Pure mathematics; Modular group; Holomorphic function; Group (periodic table); Tensor (intrinsic definition); Differential (mechanical device); Weight; Algebra over a field; Representation (politics); Combinatorics; Computer science","score_opus":0.06466379810937513,"score_gpt":0.34208933738349495,"score_spread":0.27742553927411984,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2897200622","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.88205063,0.00015168624,0.111330085,0.00015468469,0.0016035436,0.00015857202,0.00069037837,0.0000073061474,0.0038531234],"genre_scores_gemma":[0.9676249,0.00011376127,0.031629287,0.000023272338,0.000268728,0.0000024184656,0.00001046222,0.000028286231,0.00029885696],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.997963,0.000089204754,0.0009789354,0.00015858961,0.00069392484,0.00011634479],"domain_scores_gemma":[0.9952798,0.0007236979,0.002355054,0.00033722192,0.0012424297,0.00006180786],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007285642,0.00019193075,0.0006454152,0.00024962387,0.000028337217,0.00003074841,0.00064554124,0.00018429302,0.0009048128],"category_scores_gemma":[0.0012944734,0.00016632826,0.000329179,0.000046060693,0.00024773958,0.00021251854,0.00045509567,0.0005424516,0.000004922773],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00063979207,0.00037165842,0.0035189418,0.00054252765,0.003334764,0.000031191266,0.00061129633,0.00039021892,0.0019558305,0.9809508,0.00035887136,0.0072941473],"study_design_scores_gemma":[0.0011523549,0.000041183026,0.0056822905,0.0010539915,0.00017126229,0.00034872117,0.00026856296,0.00011656189,0.002903295,0.9880575,0.000054769484,0.00014951012],"about_ca_topic_score_codex":0.0000033705394,"about_ca_topic_score_gemma":0.0000018387698,"teacher_disagreement_score":0.08557431,"about_ca_system_score_codex":0.000071460745,"about_ca_system_score_gemma":0.00014720976,"threshold_uncertainty_score":0.9907066},"labels":[],"label_agreement":null},{"id":"W2897990690","doi":"10.1142/s1793042119500349","title":"On subset sums of zero-sum free sets of abelian groups","year":2018,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Brock University","funders":"Brock University; China Scholarship Council","keywords":"Mathematics; Zero (linguistics); Combinatorics; Order (exchange); Abelian group; Group (periodic table); Physics","score_opus":0.022333322951596225,"score_gpt":0.3274169057785158,"score_spread":0.30508358282691955,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2897990690","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.97870773,0.000038298065,0.0013259328,0.00014493908,0.0020187676,0.000060166225,0.0002807354,0.000009232575,0.017414207],"genre_scores_gemma":[0.9957516,0.000018496106,0.0033365437,0.00019636255,0.00039996725,8.264292e-7,0.000004628204,0.000024629122,0.00026691702],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9980044,0.00018525678,0.0007743934,0.00011116538,0.0007817751,0.00014303181],"domain_scores_gemma":[0.99636936,0.0012956379,0.000984614,0.00034518773,0.00093549065,0.0000697265],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0011142945,0.00015078431,0.00033345242,0.00021498757,0.00004447215,0.000014034089,0.0010705616,0.0000979646,0.0028930763],"category_scores_gemma":[0.0013069246,0.00011172512,0.0002732874,0.000092845614,0.000379091,0.00013849963,0.00015944905,0.00023474894,0.000012792879],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0008517211,0.00016981625,0.001480943,0.000026131038,0.00056954246,0.000028546787,0.0015244695,0.0000018886909,0.0011759481,0.97084135,0.021404468,0.0019251582],"study_design_scores_gemma":[0.00090129377,0.000227776,0.0015583625,0.00027870308,0.00004909226,0.0001891844,0.00015170318,0.000006087993,0.013601138,0.98206604,0.00086840976,0.00010223477],"about_ca_topic_score_codex":0.0000043012374,"about_ca_topic_score_gemma":0.0000046387577,"teacher_disagreement_score":0.020536058,"about_ca_system_score_codex":0.00004264834,"about_ca_system_score_gemma":0.000044429355,"threshold_uncertainty_score":0.99801844},"labels":[],"label_agreement":null},{"id":"W2898536868","doi":"10.1142/s1793042119501215","title":"The Lindelöf class of L-functions II","year":2019,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto; Queen's University","funders":"","keywords":"Mathematics; Class (philosophy); Pure mathematics; Generalization; Ring (chemistry); Invariant (physics); Integer (computer science); Noetherian ring; Combinatorics; Discrete mathematics; Algebra over a field; Commutative property; Mathematical analysis","score_opus":0.014240190718038172,"score_gpt":0.31970595685273834,"score_spread":0.30546576613470017,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2898536868","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.93947023,0.00013379405,0.012381329,0.0011996318,0.0034563134,0.00008662188,0.00004782623,0.000013264316,0.04321098],"genre_scores_gemma":[0.98632616,0.000030318843,0.0010310654,0.000119257,0.00037643395,0.0000012096692,0.0000019524846,0.000013021201,0.012100603],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99886286,0.000068474386,0.00044886032,0.000060648166,0.00046186923,0.000097284596],"domain_scores_gemma":[0.99697065,0.0016990443,0.00054196303,0.0001558843,0.00059562386,0.000036822315],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00067308755,0.00007504078,0.00014858827,0.000073921394,0.000062472114,0.000017407025,0.0004591469,0.00004304834,0.0025650149],"category_scores_gemma":[0.00070340314,0.000047550147,0.00018044609,0.00008108464,0.00007068922,0.00016087257,0.000088332876,0.00023348622,0.00011040907],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00029800998,0.00017601417,0.002013051,0.000008162227,0.00047110565,0.000009746255,0.00034073566,0.000060246515,0.0004823108,0.97390795,0.011638017,0.010594673],"study_design_scores_gemma":[0.00049913325,0.00006686482,0.00048905204,0.000078207646,0.000025316014,0.00018687204,0.0006678928,0.00002258547,0.0005831549,0.9387617,0.058558334,0.000060848026],"about_ca_topic_score_codex":3.153462e-7,"about_ca_topic_score_gemma":0.0000014273235,"teacher_disagreement_score":0.04692032,"about_ca_system_score_codex":0.00004521978,"about_ca_system_score_gemma":0.000056946563,"threshold_uncertainty_score":0.99834675},"labels":[],"label_agreement":null},{"id":"W2900154016","doi":"10.1142/s1793042120500141","title":"The arithmetic of vector-valued modular forms on Γ0(2)","year":2019,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Modular form; Component (thermodynamics); Algebra over a field; Rank (graph theory); Fourier series; Dedekind cut; Dedekind eta function; Algebraic number; Ring (chemistry)","score_opus":0.013395443896279087,"score_gpt":0.32043779476676243,"score_spread":0.3070423508704833,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2900154016","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9792508,0.00008510184,0.0062355804,0.0003549029,0.0013203665,0.00009376497,0.000023399945,0.000009333174,0.012626772],"genre_scores_gemma":[0.99638677,0.000023987372,0.001443667,0.00013133386,0.00022104196,0.0000015051659,0.0000016421084,0.000018341001,0.0017717209],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9985518,0.00008331224,0.00047622804,0.000080782804,0.00068074145,0.00012713407],"domain_scores_gemma":[0.9972051,0.0015588938,0.00056960405,0.00020350423,0.0004195574,0.000043370972],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008391116,0.00010458626,0.00020296554,0.00009367014,0.000032529846,0.000025434541,0.00056926935,0.000046109413,0.0010574335],"category_scores_gemma":[0.00086121255,0.00006196627,0.00020722057,0.00008294266,0.000067038156,0.0001510346,0.000055944274,0.0002408694,0.00011367252],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00038555768,0.00014773374,0.0005520047,0.000013033775,0.0003497539,0.000018955501,0.00018063601,0.00009571541,0.0006342426,0.9905671,0.0006995382,0.0063557103],"study_design_scores_gemma":[0.0006722929,0.000112005495,0.0013510134,0.00015849371,0.00002201041,0.00013732693,0.00026631306,0.00007998298,0.003117359,0.9910995,0.0029048526,0.00007887608],"about_ca_topic_score_codex":3.5388018e-7,"about_ca_topic_score_gemma":5.078508e-7,"teacher_disagreement_score":0.017135981,"about_ca_system_score_codex":0.000065738044,"about_ca_system_score_gemma":0.000039527,"threshold_uncertainty_score":0.99985576},"labels":[],"label_agreement":null},{"id":"W2901962487","doi":"10.1142/s1793042119500519","title":"Regulator proofs for Boyd’s identities on genus 2 curves","year":2018,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematical proof; Hypergeometric function; Genus; Elliptic curve; Measure (data warehouse); Hypergeometric distribution","score_opus":0.03569519882541698,"score_gpt":0.354977982487906,"score_spread":0.319282783662489,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2901962487","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.88886297,0.0005627014,0.026745921,0.0031002928,0.00979887,0.0007856393,0.00038232532,0.0001081846,0.069653116],"genre_scores_gemma":[0.9730971,0.000057272668,0.0038725606,0.0017856874,0.004210079,0.000030176509,0.0000128465645,0.000053904576,0.016880412],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9983398,0.00014670282,0.00056434836,0.00014022905,0.0006215395,0.00018739773],"domain_scores_gemma":[0.9966206,0.001447062,0.00058209227,0.00019741771,0.0010692474,0.000083571234],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0016298876,0.0001590655,0.00025835517,0.00020293296,0.00008140471,0.000055128497,0.0006580615,0.00007415236,0.005222489],"category_scores_gemma":[0.002141804,0.00012996545,0.0002705728,0.00009962339,0.00019526089,0.0002910733,0.00006470927,0.00017510173,0.00015986757],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0011542513,0.0002608011,0.00020394892,0.00008492573,0.00063673744,0.000037031397,0.000607423,5.551957e-7,0.00010843589,0.7851466,0.20491095,0.006848348],"study_design_scores_gemma":[0.0007254994,0.00021069041,0.00016044376,0.0006275195,0.00006453435,0.0005105881,0.00022139537,0.000004494815,0.0048936903,0.94773734,0.044700038,0.00014376729],"about_ca_topic_score_codex":4.3585518e-7,"about_ca_topic_score_gemma":7.392559e-7,"teacher_disagreement_score":0.16259074,"about_ca_system_score_codex":0.00008611275,"about_ca_system_score_gemma":0.00007594064,"threshold_uncertainty_score":0.9956869},"labels":[],"label_agreement":null},{"id":"W2902560510","doi":"10.1142/s1793042121500822","title":"Towards the Sato–Tate groups of trinomial hyperelliptic curves","year":2021,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Genus; Trinomial; Identity (music); Group (periodic table); Hyperelliptic curve; Combinatorics; Component (thermodynamics); Pure mathematics; Algebra over a field; Physics; Botany","score_opus":0.047634234651359485,"score_gpt":0.3262600989247023,"score_spread":0.27862586427334285,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2902560510","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.96542895,0.0029639306,0.007326807,0.0018134669,0.007308336,0.000278657,0.00027517046,0.000029236566,0.014575455],"genre_scores_gemma":[0.99268985,0.0015894509,0.0023575565,0.0005602081,0.0016252907,0.000012090597,0.00004677003,0.000060703773,0.0010581078],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9955911,0.00096265384,0.0015700802,0.00027114508,0.0013597411,0.0002452808],"domain_scores_gemma":[0.9926617,0.0028855617,0.0022817287,0.00057488994,0.0014840724,0.0001120306],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0036113404,0.00037514465,0.0008738775,0.00019522355,0.000055991906,0.00010086127,0.0021695832,0.0002657211,0.0046460656],"category_scores_gemma":[0.002681822,0.00026500804,0.0010146638,0.00015074229,0.00032579282,0.00019609237,0.00094539055,0.0014576308,0.000028619503],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0026306876,0.0025347457,0.0017624914,0.0026002536,0.015563693,0.0015322882,0.009806351,0.00024613604,0.00062426314,0.88562477,0.03888007,0.03819428],"study_design_scores_gemma":[0.00090268516,0.000051207386,0.0008839624,0.0032966342,0.00054010324,0.0016847987,0.002022469,0.000015441066,0.0021844099,0.98580813,0.0022788763,0.00033125438],"about_ca_topic_score_codex":0.000017178229,"about_ca_topic_score_gemma":0.0000038026428,"teacher_disagreement_score":0.10018342,"about_ca_system_score_codex":0.00015370721,"about_ca_system_score_gemma":0.0005369637,"threshold_uncertainty_score":0.9999802},"labels":[],"label_agreement":null},{"id":"W2904515035","doi":"10.1142/s179304212150024x","title":"Linear periods and distinguished local parameters","year":2020,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Conjecture; Field (mathematics); Spectrum (functional analysis); Space (punctuation); Discrete spectrum; Local field","score_opus":0.03617900491677396,"score_gpt":0.34121782143555485,"score_spread":0.3050388165187809,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2904515035","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.78196144,0.000086226515,0.21284316,0.0019620443,0.00055785786,0.000044061522,0.000036029418,0.000024420066,0.0024847363],"genre_scores_gemma":[0.97719127,0.000013573803,0.021259012,0.00091106264,0.00049142854,6.824976e-7,0.0000024161814,0.00001498837,0.0001155455],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9991293,0.000059595764,0.00032349612,0.00008993438,0.00030673173,0.00009092811],"domain_scores_gemma":[0.9986376,0.00070126285,0.00025313674,0.000054317883,0.0002321966,0.000121456345],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000248997,0.00009086213,0.00017328479,0.00003926117,0.000024878318,0.000029561676,0.00023883054,0.00003641982,0.000883511],"category_scores_gemma":[0.0021138682,0.00007324877,0.00009238622,0.000059220336,0.000108183696,0.00013303888,0.000070548514,0.0002090855,0.00002360798],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0025803205,0.00046686447,0.016088583,0.00014034675,0.0018391751,0.0017392335,0.0106983045,0.00031778097,0.0007849707,0.7601916,0.01941192,0.1857409],"study_design_scores_gemma":[0.0010786208,0.00011777205,0.0008125266,0.000114391514,0.000054070628,0.00073178456,0.0010944778,0.0005800305,0.00073488685,0.9833096,0.011185941,0.00018585804],"about_ca_topic_score_codex":4.039727e-7,"about_ca_topic_score_gemma":3.1783318e-7,"teacher_disagreement_score":0.22311805,"about_ca_system_score_codex":0.000026723506,"about_ca_system_score_gemma":0.000025619067,"threshold_uncertainty_score":0.96738255},"labels":[],"label_agreement":null},{"id":"W2907887811","doi":"10.1142/s1793042121500494","title":"A conjectural refinement of strong multiplicity one for GL(n)","year":2020,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Unitary state; Mathematics; Automorphic form; Multiplicity (mathematics); Pure mathematics; Eigenvalues and eigenvectors; Langlands program; Algebraic number field; Set (abstract data type); Field (mathematics); Mathematical analysis; Physics; Computer science","score_opus":0.10375784631745946,"score_gpt":0.403917482884738,"score_spread":0.3001596365672785,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2907887811","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.34588552,0.0002300214,0.6422718,0.0024157874,0.0031632034,0.0006165381,0.0019150417,0.00003974976,0.003462309],"genre_scores_gemma":[0.9384319,0.000027010963,0.05988299,0.00018285718,0.001137869,0.00001596811,0.000057088222,0.000036494017,0.00022778567],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9978657,0.00009242344,0.0010198815,0.00019288332,0.0006786086,0.00015053396],"domain_scores_gemma":[0.99519324,0.0015360691,0.001836224,0.00019657491,0.0011471496,0.000090730835],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00060923834,0.00022169159,0.0006026054,0.00013493616,0.00002252721,0.000029094545,0.00078728626,0.00014013176,0.0011677492],"category_scores_gemma":[0.002009079,0.00019450401,0.00052356854,0.000047147852,0.00007593401,0.000088954825,0.0004222687,0.00057798333,0.0000069530347],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.003832731,0.0010518576,0.0007379972,0.00088148663,0.005951529,0.00007688745,0.0019219392,0.00073645095,0.0018971981,0.9492171,0.00819492,0.025499938],"study_design_scores_gemma":[0.0013740794,0.00009521477,0.00023899408,0.0006786553,0.00016868171,0.00005411542,0.00025838803,0.0001426181,0.003614843,0.99193394,0.0012573816,0.00018311551],"about_ca_topic_score_codex":0.0000021860187,"about_ca_topic_score_gemma":0.0000032133664,"teacher_disagreement_score":0.5925464,"about_ca_system_score_codex":0.00015343164,"about_ca_system_score_gemma":0.00014812409,"threshold_uncertainty_score":0.9997453},"labels":[],"label_agreement":null},{"id":"W2908529263","doi":"10.1142/s1793042120500621","title":"Orthorecursive expansion of unity","year":2019,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"International Laboratory of Mirror Symmetry and Automorphic Forms, National Research University Higher School of Economics; Russian Science Foundation","keywords":"Sequence (biology); Order (exchange); Mathematics; Norm (philosophy); Combinatorics; Series (stratigraphy); Computation; Harmonic number; Sequence space; Discrete mathematics; Pure mathematics; Algorithm; Banach space; Law","score_opus":0.06425784702267033,"score_gpt":0.3994511124441252,"score_spread":0.33519326542145483,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2908529263","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.87862855,0.00025807804,0.046091266,0.00068241113,0.006289057,0.0005582246,0.00084832136,0.000037241032,0.06660687],"genre_scores_gemma":[0.9880274,0.00014685946,0.006052856,0.00008029413,0.00081639184,0.00000512527,0.000047600533,0.00007155281,0.00475191],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9954601,0.0008517995,0.0013151546,0.00025012947,0.0018837455,0.00023906062],"domain_scores_gemma":[0.99012923,0.0033813133,0.0023483674,0.0005854452,0.0034145038,0.00014116339],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0036058526,0.00030135488,0.00081227766,0.00039701493,0.000025424719,0.000053603668,0.0020316408,0.00032786228,0.008721667],"category_scores_gemma":[0.0034936701,0.00025318612,0.000693966,0.00010934761,0.0002556531,0.00016653675,0.0011164207,0.001547315,0.00014400238],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0040094545,0.001260798,0.0078079985,0.0007951007,0.0073241205,0.0007081562,0.004681981,0.0005656697,0.0006294718,0.9028718,0.056911856,0.012433582],"study_design_scores_gemma":[0.00069830974,0.00006708063,0.00029307627,0.0014996261,0.00018389766,0.00034740462,0.00086393236,0.000098077515,0.0016170671,0.99233633,0.0017694245,0.00022577867],"about_ca_topic_score_codex":0.000015104864,"about_ca_topic_score_gemma":0.0000027373535,"teacher_disagreement_score":0.10939888,"about_ca_system_score_codex":0.00031850705,"about_ca_system_score_gemma":0.00085333345,"threshold_uncertainty_score":0.999992},"labels":[],"label_agreement":null},{"id":"W2953640986","doi":"10.1142/s1793042121500226","title":"On the moments of torsion points modulo primes and their applications","year":2020,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Lethbridge","funders":"Natural Sciences and Engineering Research Council of Canada; Pacific Institute for the Mathematical Sciences","keywords":"Mathematics; Combinatorics; Algebraic number field; Prime number; Algebraic number; Torsion (gastropod); Coprime integers; Galois group; Discrete mathematics; Mathematical analysis","score_opus":0.03261538864035696,"score_gpt":0.3139993022177904,"score_spread":0.2813839135774334,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2953640986","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.85291445,0.0005624053,0.09062849,0.011392004,0.002972665,0.001298308,0.0011987248,0.00007470005,0.038958237],"genre_scores_gemma":[0.99677944,0.00013472221,0.0016027103,0.0004969801,0.00051490875,0.000025053054,0.000020362459,0.00003614907,0.00038967605],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99794,0.00036850583,0.000753184,0.00021630553,0.0005988346,0.00012318986],"domain_scores_gemma":[0.994933,0.0027867572,0.0013458462,0.0003472353,0.0004937954,0.000093381095],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001386448,0.00025840793,0.00043081347,0.00013917203,0.00005690182,0.0000501674,0.0010966263,0.00015878883,0.001590759],"category_scores_gemma":[0.0008324108,0.00016174794,0.00029671006,0.00008257238,0.00018264813,0.00008550146,0.0006373417,0.00076292746,0.000031227235],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00051751215,0.00038182206,0.00010371896,0.00010767433,0.0014159363,0.000011453805,0.0018950449,0.000011442126,0.0003362614,0.9808386,0.0080318125,0.0063487384],"study_design_scores_gemma":[0.00029577455,0.000045603927,0.00013253823,0.00047196948,0.00006662141,0.00008778404,0.00061751145,0.000029309675,0.0037320848,0.99124503,0.0031411166,0.00013464299],"about_ca_topic_score_codex":0.0000016737226,"about_ca_topic_score_gemma":1.7667644e-7,"teacher_disagreement_score":0.14386497,"about_ca_system_score_codex":0.00008141403,"about_ca_system_score_gemma":0.00009700527,"threshold_uncertainty_score":0.99932194},"labels":[],"label_agreement":null},{"id":"W2962768112","doi":"10.1142/s1793042116500846","title":"Diophantine approximation of polynomials over 𝔽q[t] satisfying a divisibility condition","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Divisibility rule; Mathematics; Diophantine approximation; Finite field; Combinatorics; Field (mathematics); Ring (chemistry); Diophantine equation; Difference polynomials; Discrete mathematics; Pure mathematics; Orthogonal polynomials","score_opus":0.081079454203023,"score_gpt":0.4135155043623672,"score_spread":0.33243605015934424,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2962768112","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.95702803,0.000039085167,0.03349836,0.0002245709,0.0005837437,0.000151324,0.00010410503,0.000017962207,0.008352803],"genre_scores_gemma":[0.9941601,0.0000074730447,0.004627546,0.000056905745,0.00045276468,0.0000037519367,0.000015962458,0.000024419129,0.0006510389],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9968012,0.00053170667,0.0010256517,0.00014597055,0.0013190273,0.00017646875],"domain_scores_gemma":[0.9953392,0.0016072564,0.0011329071,0.00023570938,0.0015356946,0.00014923497],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.004980132,0.00014734948,0.00039788167,0.00021766571,0.000028254382,0.00005055303,0.0005676338,0.000082178514,0.002916476],"category_scores_gemma":[0.0049566235,0.00012326839,0.00022417695,0.00014408916,0.00018754101,0.00051750115,0.00013882501,0.0002570073,0.000048497484],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0026924699,0.0010293976,0.030455811,0.00013321536,0.0014884415,0.0001291724,0.0034494614,0.000038900278,0.0061573717,0.9308136,0.0152036175,0.00840851],"study_design_scores_gemma":[0.0017623204,0.000072287025,0.0029344587,0.00022449857,0.00006925402,0.0002887893,0.0006469633,0.00027263054,0.0057385084,0.98750746,0.00035500558,0.00012783747],"about_ca_topic_score_codex":0.000014836083,"about_ca_topic_score_gemma":0.000003006201,"teacher_disagreement_score":0.056693815,"about_ca_system_score_codex":0.00024882818,"about_ca_system_score_gemma":0.00020621109,"threshold_uncertainty_score":0.997995},"labels":[],"label_agreement":null},{"id":"W2962907707","doi":"10.1142/s1793042111004526","title":"COMMON DIVISORS OF VALUES OF POLYNOMIALS AND COMMON FACTORS OF INDICES IN A NUMBER FIELD","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Brock University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Integer (computer science); Discriminant; Combinatorics; Prime factor; Prime (order theory); Degree (music); Field (mathematics); Algebraic number field; Polynomial; Greatest common divisor; Discrete mathematics; Pure mathematics; Mathematical analysis","score_opus":0.07222795215816397,"score_gpt":0.3820572551630411,"score_spread":0.30982930300487715,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2962907707","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9863499,0.000049961345,0.00019178564,0.000045131463,0.00014367205,0.00008214811,0.000058706348,0.0000034753891,0.013075248],"genre_scores_gemma":[0.9986865,0.000044756714,0.000968775,0.00002188852,0.00004477876,0.0000011631766,0.0000020472141,0.00001832658,0.00021175787],"study_design_codex":"observational","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99746597,0.00043472383,0.0011709433,0.000103165374,0.0006769406,0.00014825501],"domain_scores_gemma":[0.9944286,0.003634472,0.0012978901,0.00018811849,0.00037885387,0.00007210038],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0019673393,0.00014275787,0.0006282237,0.00027585292,0.000014219002,0.000009239371,0.000673198,0.000104683466,0.003253879],"category_scores_gemma":[0.0010196452,0.00011453661,0.00018919064,0.0001231773,0.00031541323,0.00022379143,0.00019119291,0.00029234227,0.0000037287202],"study_design_candidate":"observational","study_design_consensus":null,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0011334443,0.0007096458,0.8917123,0.000116702424,0.00069192005,0.00003595207,0.010225874,0.0000014552281,0.0006968122,0.09246323,0.0004475322,0.0017651492],"study_design_scores_gemma":[0.001116401,0.00020218332,0.07593853,0.0007232018,0.000087345165,0.00011162204,0.0039019445,0.000016574326,0.042747468,0.87497866,0.000037433118,0.00013866262],"about_ca_topic_score_codex":0.00035347085,"about_ca_topic_score_gemma":0.000067671026,"teacher_disagreement_score":0.8157737,"about_ca_system_score_codex":0.00004216295,"about_ca_system_score_gemma":0.0000667967,"threshold_uncertainty_score":0.9976573},"labels":[],"label_agreement":null},{"id":"W2963867932","doi":"10.1142/s1793042118500276","title":"The size function for cyclic cubic fields","year":2017,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Calgary","funders":"National Natural Science Foundation of China; Fundamental Research Funds for the Central Universities; Pacific Institute for the Mathematical Sciences","keywords":"Mathematics; Conjecture; Rank (graph theory); Algebraic number field; Dimension (graph theory); Riemann hypothesis; Function field; Pure mathematics; Unit (ring theory); Algebraic curve; Algebraic number; Field (mathematics); Combinatorics; Function (biology); Mathematical analysis","score_opus":0.03091272230319816,"score_gpt":0.34941274293175645,"score_spread":0.3185000206285583,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2963867932","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.76204807,0.00030286986,0.11704257,0.011999868,0.02004169,0.00047761464,0.00008737805,0.00006561808,0.08793429],"genre_scores_gemma":[0.9875695,0.000038284987,0.0011258625,0.00032945463,0.0016536209,0.000010643311,0.0000015953531,0.0000196289,0.009251395],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99880284,0.000111169895,0.000436142,0.00009613882,0.00039150575,0.00016219485],"domain_scores_gemma":[0.9923459,0.0058444263,0.0008865979,0.000344398,0.0005181446,0.000060513506],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0020940145,0.0001146413,0.00016801582,0.000034814606,0.00047742773,0.00022547784,0.0011558866,0.00008475004,0.0014300175],"category_scores_gemma":[0.0074193245,0.00007543177,0.00028589286,0.000020419726,0.00015567658,0.00032693986,0.000099589844,0.00024212783,0.0000513624],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0015752673,0.00011694189,0.00069826946,0.000012233705,0.000759084,0.000020629761,0.00027047985,0.0000021108183,0.00013130838,0.9223764,0.04050503,0.033532247],"study_design_scores_gemma":[0.00074141263,0.000059100174,0.001752102,0.00005687808,0.00006460185,0.00019132743,0.0002501495,0.000008179644,0.00053936144,0.93907773,0.057174034,0.00008510681],"about_ca_topic_score_codex":0.0000020218108,"about_ca_topic_score_gemma":0.0000043848327,"teacher_disagreement_score":0.22552142,"about_ca_system_score_codex":0.000046953508,"about_ca_system_score_gemma":0.00004988259,"threshold_uncertainty_score":0.9994828},"labels":[],"label_agreement":null},{"id":"W2963908401","doi":"10.1142/s1793042115501080","title":"Representations by octonary quadratic forms with coefficients 1, 3 or 9","year":2015,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Modular form; Eisenstein series; Diagonal; Quadratic equation; Integer (computer science); Binary quadratic form; Pure mathematics; ε-quadratic form; Quadratic field; Combinatorics; Arithmetic; Algebra over a field; Quadratic function; Geometry","score_opus":0.05910812617871217,"score_gpt":0.3958007046831956,"score_spread":0.3366925785044834,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2963908401","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.20057298,0.00013068428,0.68444157,0.0013876435,0.0012060372,0.0004010014,0.00023732247,0.00011062952,0.11151213],"genre_scores_gemma":[0.9087337,0.00001941502,0.050010614,0.00032557402,0.00030022464,0.000020483707,0.000028746288,0.00007211405,0.040489078],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9981416,0.00009095654,0.00055582717,0.00010672907,0.000958072,0.00014684412],"domain_scores_gemma":[0.9969949,0.0013363629,0.00049590995,0.00016825588,0.00085461745,0.00014996776],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.000589978,0.0001318901,0.00023404481,0.00009273057,0.000036498164,0.00007563122,0.00047667016,0.00004076851,0.0017323493],"category_scores_gemma":[0.0022039805,0.00008185067,0.00008411933,0.00010473707,0.00014374746,0.0005768856,0.0000751529,0.00017679115,0.000091474314],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0023262755,0.0015579043,0.00077995035,0.00006491897,0.001035233,0.0007115517,0.0040778387,0.00019213077,0.00019961115,0.7832628,0.2040861,0.001705729],"study_design_scores_gemma":[0.0012320828,0.00013158399,0.00001658646,0.00020820084,0.000058170946,0.001429911,0.0034055184,0.00005397088,0.00053126464,0.9858271,0.0069742445,0.00013135932],"about_ca_topic_score_codex":0.0000020530913,"about_ca_topic_score_gemma":0.0000051696716,"teacher_disagreement_score":0.70816076,"about_ca_system_score_codex":0.0001423019,"about_ca_system_score_gemma":0.00014389373,"threshold_uncertainty_score":0.9991802},"labels":[],"label_agreement":null},{"id":"W2963956968","doi":"10.1142/s1793042111004319","title":"THE SUM OF DIGITS OF n AND n<sup>2</sup>","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada; Agence Nationale de la Recherche","keywords":"Mathematics; Combinatorics; Integer (computer science); Discrete mathematics","score_opus":0.06196038668767846,"score_gpt":0.3514113979168523,"score_spread":0.2894510112291738,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2963956968","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.935504,0.00017463931,0.0027097205,0.00023548846,0.00019880265,0.0001018356,0.000058408477,0.0000075823395,0.061009478],"genre_scores_gemma":[0.99617374,0.00009138564,0.0014437583,0.00002435658,0.00012252117,0.0000013375812,7.8058855e-7,0.000018123203,0.0021239896],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9981044,0.00024350779,0.0007021337,0.00008221046,0.0007223279,0.00014544759],"domain_scores_gemma":[0.99549645,0.002623092,0.0006426144,0.00019950235,0.0009611079,0.00007722553],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0022595846,0.0001029491,0.0002564699,0.000101793965,0.000038067697,0.000021613934,0.000763655,0.00005060829,0.0015178089],"category_scores_gemma":[0.0017638396,0.00006595855,0.00016174043,0.00007852394,0.00044417454,0.00018242552,0.00016688873,0.00022122714,0.000013874074],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0010175236,0.00029222865,0.009207398,0.000037093512,0.0010882844,0.0000514959,0.003856227,0.0000036252773,0.00015550903,0.9709438,0.0033922188,0.009954596],"study_design_scores_gemma":[0.0005750118,0.000074960335,0.000973459,0.00016621091,0.000054484044,0.0003839407,0.0018049093,0.00010259692,0.0023632383,0.9916856,0.0017433963,0.00007218402],"about_ca_topic_score_codex":0.000008775386,"about_ca_topic_score_gemma":0.0000023218556,"teacher_disagreement_score":0.0606697,"about_ca_system_score_codex":0.00003384938,"about_ca_system_score_gemma":0.00008933784,"threshold_uncertainty_score":0.99939495},"labels":[],"label_agreement":null},{"id":"W2963982562","doi":"10.1142/s1793042111004411","title":"A REFINEMENT OF KOBLITZ'S CONJECTURE","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":22,"is_retracted":false,"has_abstract":true,"route_ca_aff":false,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Conjecture; Elliptic curve; Sato–Tate conjecture; Modulo; Constant (computer programming); Integer (computer science); Rational number; Prime (order theory); Cardinality (data modeling); Asymptotic formula; abc conjecture; Combinatorics; Discrete mathematics; Modular elliptic curve; Infinity; Number theory; Prime number; Collatz conjecture; Pure mathematics; Mathematical analysis","score_opus":0.050378346950456884,"score_gpt":0.3188077562945137,"score_spread":0.2684294093440568,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2963982562","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7794003,0.00019562533,0.02315338,0.00038053349,0.0024873617,0.0001356623,0.00010946822,0.00003415857,0.19410352],"genre_scores_gemma":[0.98905313,0.00001697904,0.008859954,0.00017753775,0.000294798,0.000001937176,0.0000029693947,0.000018224746,0.0015744839],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9983848,0.00017695883,0.0006853194,0.000093115974,0.00053126214,0.00012855814],"domain_scores_gemma":[0.99771285,0.0006858194,0.000803631,0.00017984747,0.0005448551,0.00007297249],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0013201348,0.0001285777,0.000273124,0.00015866349,0.000020259316,0.000010125618,0.0006219106,0.0000759449,0.030376352],"category_scores_gemma":[0.0007825191,0.00009967256,0.00023514095,0.00010144561,0.00011834161,0.00015888322,0.00008495888,0.00022822723,0.000063420026],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00084897754,0.00050307845,0.0014411167,0.000027931084,0.0008699841,0.00013954873,0.0029535869,6.792258e-7,0.00031597048,0.9767677,0.010897247,0.0052341493],"study_design_scores_gemma":[0.0007570145,0.00009985998,0.0009570243,0.0001496385,0.00006662416,0.0006919093,0.00068019365,8.4799876e-7,0.0075850664,0.98205477,0.0068537034,0.00010334392],"about_ca_topic_score_codex":0.0000043884183,"about_ca_topic_score_gemma":9.652756e-7,"teacher_disagreement_score":0.20965283,"about_ca_system_score_codex":0.00004642674,"about_ca_system_score_gemma":0.000065671346,"threshold_uncertainty_score":0.97051},"labels":[],"label_agreement":null},{"id":"W2964118337","doi":"10.1142/s1793042111004472","title":"A REFINED MODULAR APPROACH TO THE DIOPHANTINE EQUATION x<sup>2</sup> + y<sup>2n</sup> = z<sup>3</sup>","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Diophantine equation; Integer (computer science); Mathematics; Coprime integers; Fermat's Last Theorem; Modular form; Number theory; Diophantine set; Galois module; Prime (order theory); Type (biology); Discrete mathematics; Combinatorics; Pure mathematics","score_opus":0.04951312201273072,"score_gpt":0.2864905686183558,"score_spread":0.23697744660562509,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2964118337","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8207733,0.0002668429,0.12326056,0.0019230713,0.00082778046,0.0007926552,0.00022550681,0.00017142907,0.051758856],"genre_scores_gemma":[0.9751461,0.000049122107,0.0149541935,0.0015214826,0.0024033065,0.00006562758,0.00007711589,0.00015136995,0.00563164],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99349385,0.0011802645,0.0018852919,0.0006267142,0.0020652313,0.00074866915],"domain_scores_gemma":[0.9942762,0.0018460081,0.0011506872,0.00095661066,0.0013599482,0.0004105056],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.005748754,0.0006674914,0.0008754572,0.00058560976,0.00032598226,0.00021580618,0.0025945078,0.0003446,0.005841352],"category_scores_gemma":[0.003248465,0.0005103017,0.0007469196,0.00064185145,0.00028935925,0.0009202261,0.0005020394,0.0011437576,0.00095481623],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.004988009,0.0036614197,0.0012670583,0.00018970492,0.0044098846,0.00043050086,0.05064741,0.02198443,0.00026651233,0.8640294,0.031572513,0.016553165],"study_design_scores_gemma":[0.0040013175,0.00037894057,0.00069932244,0.0006176856,0.0005770946,0.0030089442,0.010125793,0.02872437,0.0012821109,0.9225593,0.026899483,0.0011255965],"about_ca_topic_score_codex":0.000029103858,"about_ca_topic_score_gemma":0.0000013322216,"teacher_disagreement_score":0.15437284,"about_ca_system_score_codex":0.00029306512,"about_ca_system_score_gemma":0.00019777323,"threshold_uncertainty_score":0.99982303},"labels":[],"label_agreement":null},{"id":"W2964281852","doi":"10.1142/s1793042113500012","title":"MINIMAL ZERO-SUM SEQUENCES OF LENGTH FOUR OVER FINITE CYCLIC GROUPS II","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Brock University","funders":"Civil Aviation University of China; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Mathematics; Combinatorics; Cyclic group; Order (exchange); Sequence (biology); Prime (order theory); Product (mathematics); Zero (linguistics); Finite group; Group (periodic table); Discrete mathematics; Abelian group; Geometry","score_opus":0.030592489644625333,"score_gpt":0.2958538145450977,"score_spread":0.26526132490047233,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2964281852","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.98985493,0.000078062,0.0020872161,0.00042275025,0.0008696629,0.00007038263,0.00003360599,0.000014669683,0.006568729],"genre_scores_gemma":[0.9921317,0.000052282525,0.0051945723,0.00024406408,0.0006786083,0.0000045419033,0.000003259925,0.000025651081,0.0016652828],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9981041,0.00012253322,0.0007554899,0.00012868758,0.0007074553,0.00018172024],"domain_scores_gemma":[0.99723,0.0011441287,0.0008435139,0.00015637524,0.0005354598,0.000090544694],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0006412365,0.00016293424,0.00030529365,0.00014385564,0.000050457373,0.00005521053,0.0006597863,0.0000791058,0.0066485773],"category_scores_gemma":[0.000725265,0.00012869335,0.00026596637,0.00005777189,0.00014284377,0.00056651887,0.00012435082,0.0002607073,0.000116568706],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00058983173,0.001451794,0.018573266,0.00013031512,0.0021610425,0.0003118303,0.0066347206,0.00007803677,0.024431484,0.85201436,0.070883125,0.022740176],"study_design_scores_gemma":[0.00078715273,0.0001108071,0.006767025,0.0002863721,0.00005037901,0.00039700296,0.0003350834,0.000071680864,0.0040539396,0.98388034,0.0030827126,0.0001774977],"about_ca_topic_score_codex":0.000018355362,"about_ca_topic_score_gemma":0.0000032061068,"teacher_disagreement_score":0.13186596,"about_ca_system_score_codex":0.00006455191,"about_ca_system_score_gemma":0.00006522003,"threshold_uncertainty_score":0.9942595},"labels":[],"label_agreement":null},{"id":"W2966126475","doi":"10.1142/s1793042120500207","title":"Adaptation of Monsky matrices for 𝜃-congruent numbers","year":2019,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Generalization; Combinatorics; Order (exchange)","score_opus":0.04481728084854394,"score_gpt":0.37498203943845104,"score_spread":0.3301647585899071,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2966126475","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.91485107,0.00013761714,0.06122968,0.00049358665,0.0016450131,0.00046827746,0.00019001839,0.000022268841,0.020962479],"genre_scores_gemma":[0.97973704,0.00003513828,0.014393454,0.000062880994,0.00030901493,0.000007971692,0.000010583258,0.00003572943,0.0054081967],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99783736,0.00017387538,0.0007832193,0.00013078428,0.0008935876,0.00018117759],"domain_scores_gemma":[0.99425435,0.0030858195,0.00092387473,0.00019124993,0.0014631932,0.00008154121],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002074178,0.00013213244,0.00033438264,0.00021157747,0.000023083643,0.00003596951,0.0007228806,0.00007332204,0.005153785],"category_scores_gemma":[0.0011761177,0.00011113644,0.0003342767,0.000113122034,0.00008457086,0.0003100311,0.000071259245,0.00018826473,0.00011645713],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0025439232,0.00051640475,0.0090960795,0.00017449322,0.0017536278,0.000034935238,0.0019638194,0.00030784684,0.0010319591,0.95629936,0.013138858,0.013138689],"study_design_scores_gemma":[0.002044606,0.00014882367,0.00026875714,0.00030090025,0.00011306591,0.00025676462,0.0030585849,0.001138121,0.0017185634,0.97932595,0.011455063,0.00017079864],"about_ca_topic_score_codex":0.000015718868,"about_ca_topic_score_gemma":0.0000059251815,"teacher_disagreement_score":0.064885974,"about_ca_system_score_codex":0.00014200002,"about_ca_system_score_gemma":0.00016246628,"threshold_uncertainty_score":0.9957556},"labels":[],"label_agreement":null},{"id":"W2968624656","doi":"10.1142/s1793042120400096","title":"Polynomial analogues of restricted multicolor b-ary partition functions","year":2020,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Lambda; Partition (number theory); Mathematics; Combinatorics; Factorization; Integer (computer science); Polynomial; Sequence (biology); Base (topology); Discrete mathematics; Physics; Algorithm; Computer science","score_opus":0.07106510291960451,"score_gpt":0.370228220814853,"score_spread":0.2991631178952485,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2968624656","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7145891,0.00038888576,0.22231765,0.0043967017,0.035541188,0.0014802994,0.0035719802,0.00032661736,0.017387554],"genre_scores_gemma":[0.9673788,0.000064248205,0.0297841,0.000101381214,0.0021755777,0.000019851615,0.00010721379,0.00006608782,0.00030276782],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9969361,0.00030375502,0.0014850869,0.00021146586,0.00090251054,0.00016111709],"domain_scores_gemma":[0.9932514,0.002129482,0.0026923309,0.0003082573,0.0014591282,0.00015942373],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00049069664,0.0002761064,0.0006778543,0.0002464423,0.00003569499,0.000050336817,0.0009198091,0.00026263887,0.0011055912],"category_scores_gemma":[0.006722632,0.0002574221,0.00048536307,0.00012897293,0.00013279011,0.00019251357,0.00050041266,0.0009308502,0.000040824943],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.008054973,0.005366343,0.0011372891,0.0013892562,0.011017661,0.0010320052,0.0066581806,0.0019019688,0.011774074,0.540916,0.4024342,0.008317986],"study_design_scores_gemma":[0.0011330341,0.00011330077,0.00025153236,0.00076611014,0.0003249438,0.00011238858,0.00034396682,0.00025205346,0.0017459207,0.99161327,0.0031096297,0.00023387239],"about_ca_topic_score_codex":0.0000052602522,"about_ca_topic_score_gemma":0.0000020801906,"teacher_disagreement_score":0.45069718,"about_ca_system_score_codex":0.00026716737,"about_ca_system_score_gemma":0.00038042184,"threshold_uncertainty_score":0.9999878},"labels":[],"label_agreement":null},{"id":"W2970908236","doi":"10.1142/s1793042120500244","title":"Norm-compatible systems of cohomology classes for GU(2,2)","year":2019,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université Laval","funders":"Engineering and Physical Sciences Research Council","keywords":"Shimura variety; Mathematics; Cohomology; Symplectic geometry; Pure mathematics; Unitary state; Algebra over a field; TRACE (psycholinguistics); Norm (philosophy); Variety (cybernetics); Modular form; Siegel modular form; Linguistics","score_opus":0.024556223622780423,"score_gpt":0.3539894033543051,"score_spread":0.3294331797315247,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2970908236","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.93757564,0.00015779771,0.050578713,0.00013295391,0.0031368874,0.00018807196,0.00012378214,0.000011778407,0.0080943545],"genre_scores_gemma":[0.9925128,0.000013193173,0.004912764,0.000072978764,0.00036726551,0.000004517121,0.0000069942676,0.000018051052,0.002091396],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9988085,0.0000713463,0.00057987124,0.00008330012,0.0003382929,0.000118664895],"domain_scores_gemma":[0.9959517,0.0022635397,0.000793482,0.00012610892,0.0008246113,0.00004057531],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005865108,0.0000953462,0.0003257258,0.00014286743,0.000013987905,0.000015468211,0.0004041102,0.00006281175,0.0012214433],"category_scores_gemma":[0.00059955346,0.00007631878,0.00017436223,0.000063233885,0.000047803285,0.0001814409,0.000041566578,0.00012565458,0.00004689557],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0004011109,0.00022389859,0.013609335,0.00012373232,0.000575103,0.000013887472,0.00023307012,0.00019960324,0.0011747722,0.9749214,0.0073777167,0.0011463742],"study_design_scores_gemma":[0.0014181319,0.00017139163,0.0008969631,0.00025899586,0.00004865891,0.00053580815,0.00062378065,0.00011063637,0.001734432,0.9838166,0.010263046,0.00012153193],"about_ca_topic_score_codex":0.0000013987233,"about_ca_topic_score_gemma":0.0000010586377,"teacher_disagreement_score":0.05493718,"about_ca_system_score_codex":0.000054339507,"about_ca_system_score_gemma":0.000062018946,"threshold_uncertainty_score":0.99969155},"labels":[],"label_agreement":null},{"id":"W2970948195","doi":"10.1142/s1793042120500293","title":"Analytic continuation for multiple zeta values using symbolic representations","year":2019,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Dalhousie University","funders":"","keywords":"Mathematics; Analytic continuation; Continuation; Riemann zeta function; Representation (politics); Pure mathematics; Computation; Harmonic number; Extension (predicate logic); Bernoulli's principle; Generating function; Harmonic function; Harmonic; Applied mathematics; Algebra over a field; Mathematical analysis; Algorithm; Computer science","score_opus":0.0650515843583139,"score_gpt":0.42213730492132506,"score_spread":0.35708572056301113,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2970948195","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.6873301,0.000042852447,0.30411753,0.00021618255,0.0013957733,0.00038146772,0.000095349584,0.000032903787,0.00638781],"genre_scores_gemma":[0.92366743,0.00000816081,0.06901295,0.000066498156,0.00044464658,0.000008321535,0.000012092757,0.000035102526,0.0067447918],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99852467,0.00009168747,0.00064330274,0.0001185691,0.00048788034,0.00013390728],"domain_scores_gemma":[0.9945111,0.0036112186,0.00067991274,0.00017041023,0.0009763187,0.00005099305],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007638093,0.00011228052,0.00027621354,0.00015267647,0.000040786814,0.000076194854,0.0003537501,0.000047462887,0.0014370164],"category_scores_gemma":[0.0039292416,0.00009903328,0.00024048932,0.00006990009,0.00005837468,0.0005222866,0.000055051372,0.00011860531,0.000058529273],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00041056835,0.00040570652,0.005977826,0.00013038602,0.0012300463,0.000022477554,0.002587964,0.0010341211,0.006477662,0.9753712,0.005348535,0.0010035412],"study_design_scores_gemma":[0.00093392073,0.00002361436,0.00031047734,0.00020759301,0.00011342241,0.00015158442,0.0010648732,0.004914752,0.0014834523,0.990261,0.00042782418,0.00010748538],"about_ca_topic_score_codex":0.0000030518027,"about_ca_topic_score_gemma":0.0000022920626,"teacher_disagreement_score":0.23633732,"about_ca_system_score_codex":0.00012519717,"about_ca_system_score_gemma":0.000056081364,"threshold_uncertainty_score":0.9994758},"labels":[],"label_agreement":null},{"id":"W2971722553","doi":"10.1142/s1793042119500829","title":"Distribution and non-vanishing of special values of L-series attached to Erdős functions","year":2019,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Conjecture; Arithmetic function; Distribution (mathematics); Limiting; Function (biology); Integer (computer science); Parity (physics); Series (stratigraphy)","score_opus":0.026486238321996307,"score_gpt":0.350571406783372,"score_spread":0.3240851684613757,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2971722553","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.97314256,0.000013247227,0.0152326105,0.00031618224,0.0006845441,0.00011898008,0.0002102331,0.0000053990693,0.01027622],"genre_scores_gemma":[0.994139,0.000009622169,0.0019234567,0.000021398057,0.0006580239,0.0000014251373,0.000012854798,0.000016029673,0.003218185],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99825746,0.00015510693,0.00062701554,0.00011126087,0.00071737973,0.00013176391],"domain_scores_gemma":[0.9972715,0.0010309039,0.00050390186,0.00015856822,0.00094818784,0.00008694937],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0015077399,0.000107849584,0.00032473705,0.00012049119,0.000027796857,0.00003292085,0.000384098,0.00005770327,0.003335899],"category_scores_gemma":[0.0012743969,0.00009274287,0.00015222708,0.00011988234,0.00013904498,0.00034047427,0.00015485846,0.00020329248,0.000053156917],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0051581142,0.0008508192,0.09221836,0.00024154576,0.0023294853,0.0000626382,0.006546045,0.00011206586,0.013120375,0.8359445,0.036577445,0.006838612],"study_design_scores_gemma":[0.00144682,0.00034265875,0.01647397,0.000586227,0.00013717625,0.0004272386,0.004912915,0.00006499196,0.0091970125,0.9622417,0.0039567663,0.000212532],"about_ca_topic_score_codex":0.0000062015765,"about_ca_topic_score_gemma":0.0000039686024,"teacher_disagreement_score":0.1262972,"about_ca_system_score_codex":0.00009973677,"about_ca_system_score_gemma":0.00009277847,"threshold_uncertainty_score":0.99757516},"labels":[],"label_agreement":null},{"id":"W2976679270","doi":"10.1142/s1793042120501031","title":"A class of maximally singular sets for rational approximation","year":2020,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Numerical Analysis Techniques","field":"Engineering","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Ottawa","funders":"","keywords":"Mathematics; Class (philosophy); Exponent; Quadratic equation; Pure mathematics; Combinatorics; Value (mathematics); Discrete mathematics; Mathematical analysis; Geometry","score_opus":0.014345873351438313,"score_gpt":0.283359894418013,"score_spread":0.2690140210665747,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2976679270","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"methods","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.011753067,0.000050929026,0.98504794,0.0010239424,0.00015468545,0.000072962815,0.00006667268,0.000047555743,0.001782233],"genre_scores_gemma":[0.8943632,0.000022251035,0.10502387,0.00027136164,0.00024438495,0.000006535366,0.000033137,0.000019696801,0.000015557302],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99904555,0.000027568558,0.0004662864,0.000064946515,0.0003236002,0.000072018076],"domain_scores_gemma":[0.9989985,0.00017505117,0.00024058149,0.000047541147,0.00048478923,0.000053500928],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00020108653,0.00008425332,0.00018174926,0.00007526797,0.00001107409,0.000016337315,0.00026538857,0.000039376304,0.00035654227],"category_scores_gemma":[0.00030458014,0.00007757835,0.0001712416,0.00009264412,0.000034513218,0.00023949733,0.000020267771,0.000109151435,0.0000066035664],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0029066298,0.00056174776,0.0014577886,0.00039347121,0.004666174,0.000109039545,0.0031121164,0.13386938,0.20944533,0.325154,0.03768032,0.280644],"study_design_scores_gemma":[0.0020745057,0.00030015942,0.00051785575,0.00023854084,0.0001894603,0.0002205479,0.00028673123,0.21701004,0.101377,0.60474026,0.07254667,0.00049823354],"about_ca_topic_score_codex":2.4114468e-7,"about_ca_topic_score_gemma":1.7242442e-7,"teacher_disagreement_score":0.88261014,"about_ca_system_score_codex":0.00006335409,"about_ca_system_score_gemma":0.000023609391,"threshold_uncertainty_score":0.3903888},"labels":[],"label_agreement":null},{"id":"W2981754859","doi":"10.1142/s1793042120500372","title":"Universal Fourier expansions of Bianchi modular forms","year":2019,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Modular form; Action (physics); Hecke operator; Modular design; Algebra over a field; Fourier series; Automorphic form; Quadratic equation; Euclidean geometry","score_opus":0.019950729947779158,"score_gpt":0.3241144008671401,"score_spread":0.304163670919361,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2981754859","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9150794,0.000037714522,0.04415363,0.00021787078,0.0009602317,0.00011394349,0.000060333714,0.000019051304,0.039357826],"genre_scores_gemma":[0.9615692,0.000021935488,0.029389746,0.000052318428,0.00016245001,0.0000012417007,0.0000028404008,0.000027788523,0.008772509],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9985655,0.000057521007,0.0005359797,0.00008095833,0.00063890027,0.00012116221],"domain_scores_gemma":[0.99763614,0.0009819979,0.0005693758,0.00019009046,0.00056003686,0.00006235206],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00046457915,0.00010693834,0.00027661043,0.00013488335,0.000016711549,0.00001853343,0.0004890295,0.000054044365,0.006045914],"category_scores_gemma":[0.00076378154,0.00008403065,0.00022075485,0.00006406234,0.00008879809,0.0004761458,0.00010311479,0.00018214878,0.00011473096],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00013739706,0.00019462174,0.00036153782,0.000040851904,0.0003376034,0.000047814316,0.00073711417,0.000067092944,0.0016006986,0.99408156,0.0017962771,0.0005974143],"study_design_scores_gemma":[0.0006437756,0.00004255756,0.00012278963,0.00028961134,0.00003849069,0.00019887548,0.0012082276,0.00010667123,0.0021427413,0.9933415,0.0017749928,0.00008975749],"about_ca_topic_score_codex":0.0000012711978,"about_ca_topic_score_gemma":0.0000010795212,"teacher_disagreement_score":0.046489775,"about_ca_system_score_codex":0.00007966138,"about_ca_system_score_gemma":0.000060346723,"threshold_uncertainty_score":0.9948627},"labels":[],"label_agreement":null},{"id":"W2985026801","doi":"10.1142/s1793042120500529","title":"Variance of sums in arithmetic progressions of divisor functions associated with higher degree L-functions in 𝔽q[t]","year":2019,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Western University","funders":"Engineering and Physical Sciences Research Council","keywords":"Mathematics; Degree (music); Divisor (algebraic geometry); Divisor function; Function (biology); Arithmetic progression; Pure mathematics; Arithmetic; Combinatorics","score_opus":0.05218959992299376,"score_gpt":0.3489533729171619,"score_spread":0.2967637729941681,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2985026801","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9703452,0.000054143988,0.0056293537,0.00037038242,0.0005804013,0.0002985517,0.00013267035,0.000012923328,0.02257637],"genre_scores_gemma":[0.98986876,0.000005114809,0.0011549266,0.00001986028,0.000061799474,0.000012098602,0.000010822579,0.000029254028,0.008837375],"study_design_codex":"observational","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9972586,0.0004556474,0.0009408239,0.0001632759,0.0009533827,0.0002282892],"domain_scores_gemma":[0.99513096,0.0027352045,0.00085938175,0.00024642842,0.0009551926,0.00007280736],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0019727678,0.0001553689,0.0004726128,0.00048512925,0.000021025913,0.000019108244,0.0005500941,0.00010449876,0.005822883],"category_scores_gemma":[0.0013947681,0.00011905115,0.00016053008,0.0005420429,0.00019970739,0.00027422945,0.00010112555,0.00053931103,0.0000450252],"study_design_candidate":"observational","study_design_consensus":null,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0021436117,0.00413924,0.70240843,0.00009846308,0.0017595866,0.0001963751,0.0012613389,0.0004906344,0.000976611,0.28182176,0.002050884,0.002653097],"study_design_scores_gemma":[0.008340248,0.00060462434,0.31719962,0.004960626,0.0002401393,0.00031327494,0.0025537536,0.00057502417,0.00049792265,0.6630356,0.0012070425,0.00047217705],"about_ca_topic_score_codex":0.000024916857,"about_ca_topic_score_gemma":0.000130104,"teacher_disagreement_score":0.38520882,"about_ca_system_score_codex":0.00024437046,"about_ca_system_score_gemma":0.00025115302,"threshold_uncertainty_score":0.99508595},"labels":[],"label_agreement":null},{"id":"W2988096628","doi":"10.1142/s1793042121500445","title":"Deformations of certain reducible Galois representations III","year":2020,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Indecomposable module; Mathematics; Galois module; Prime (order theory); Image (mathematics); Combinatorics; Pure mathematics; Computer science","score_opus":0.05505049144445941,"score_gpt":0.3651936990097504,"score_spread":0.310143207565291,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2988096628","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.5468634,0.00056061614,0.23822582,0.010110999,0.01223746,0.0010651756,0.0024742156,0.00020606724,0.1882563],"genre_scores_gemma":[0.98305255,0.00010412989,0.013190028,0.00022654788,0.0010936572,0.000017626611,0.00013526075,0.000053826523,0.002126391],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9962004,0.00046234505,0.0017819582,0.0002649835,0.0010876656,0.00020264056],"domain_scores_gemma":[0.9930163,0.0020739527,0.002688905,0.00049964536,0.0015490515,0.00017216116],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0017041629,0.0003006332,0.00069116923,0.00039626978,0.00006631555,0.00007658815,0.0015233558,0.00025628967,0.0076245544],"category_scores_gemma":[0.0033319276,0.0002770219,0.00071102445,0.00022875187,0.00019969088,0.00033204776,0.0006943126,0.0010690539,0.00008476936],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0011797366,0.0008283113,0.00071814907,0.00034587737,0.004267518,0.00018780559,0.010755378,0.0007025503,0.0005672188,0.9040371,0.0722772,0.004133147],"study_design_scores_gemma":[0.000779571,0.000036865236,0.00022578333,0.0005979264,0.0002589399,0.0004624022,0.0023913563,0.00006762597,0.0027351193,0.98956174,0.002647714,0.00023493568],"about_ca_topic_score_codex":0.000025343736,"about_ca_topic_score_gemma":0.0000026730977,"teacher_disagreement_score":0.43618917,"about_ca_system_score_codex":0.00017910522,"about_ca_system_score_gemma":0.00043301185,"threshold_uncertainty_score":0.9999682},"labels":[],"label_agreement":null},{"id":"W2989872056","doi":"10.1142/s1793042122500208","title":"Mordell–Weil ranks and Tate–Shafarevich groups of elliptic curves with mixed-reduction type over cyclotomic extensions","year":2021,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université Laval","funders":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Mathematics; Dual polyhedron; Elliptic curve; Pure mathematics; Bounded function; Torsion (gastropod); Algebra over a field; Discrete mathematics; Mathematical analysis","score_opus":0.022681929115086347,"score_gpt":0.31232042254642506,"score_spread":0.28963849343133874,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2989872056","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.98797834,0.0036523037,0.0033398196,0.0002673166,0.0030937197,0.00022092668,0.00009806915,0.000024354484,0.0013251273],"genre_scores_gemma":[0.9902709,0.0034989335,0.0043594297,0.00014253659,0.0007201503,0.0000086140535,0.00008007115,0.000071916606,0.00084745925],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99688417,0.0005241743,0.0010980888,0.00034679228,0.00093417225,0.00021261965],"domain_scores_gemma":[0.994737,0.0011803479,0.0016732106,0.0004219797,0.0018517983,0.00013563696],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001610818,0.00038167628,0.00083838956,0.0002729404,0.00005420942,0.00007742405,0.0006442119,0.0002577364,0.0034328804],"category_scores_gemma":[0.0009968497,0.00031091893,0.00030877028,0.00018835076,0.00029817474,0.00027400895,0.00045852704,0.0010432001,0.000012943324],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.026872635,0.012069026,0.024956755,0.01848235,0.056449313,0.0056615844,0.025841584,0.0040144306,0.016016623,0.65380454,0.11849917,0.037332],"study_design_scores_gemma":[0.0022757035,0.00021941967,0.004944111,0.013224206,0.001434735,0.009009445,0.0026361344,0.000103407714,0.0026701216,0.9616891,0.00097598304,0.0008176352],"about_ca_topic_score_codex":0.000013131182,"about_ca_topic_score_gemma":0.0000041525227,"teacher_disagreement_score":0.30788457,"about_ca_system_score_codex":0.00011462511,"about_ca_system_score_gemma":0.00030343476,"threshold_uncertainty_score":0.9999343},"labels":[],"label_agreement":null},{"id":"W2994621635","doi":"10.1142/s1793042121500317","title":"On the co-factors of degree 6 Salem number beta expansions","year":2020,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada; University of Waterloo","keywords":"Degree (music); Combinatorics; BETA (programming language); Mathematics; TRACE (psycholinguistics); Sequence (biology); Series (stratigraphy); Discrete mathematics; Physics","score_opus":0.11348726047059086,"score_gpt":0.38020179350909145,"score_spread":0.26671453303850057,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2994621635","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8161261,0.000040020444,0.03342266,0.0057053585,0.0035651277,0.00051509397,0.0020824838,0.000047907684,0.1384952],"genre_scores_gemma":[0.99443746,0.000046824793,0.0037660357,0.0003818446,0.00046218032,0.000008389074,0.00004555419,0.000065608045,0.00078612985],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9966371,0.00034277508,0.0013010543,0.00021375503,0.0013251287,0.0001801854],"domain_scores_gemma":[0.9887689,0.008005129,0.0019097554,0.0004522813,0.0007162925,0.00014766569],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0012473366,0.00033395886,0.00071168033,0.00009620915,0.00004812066,0.00008653107,0.0016450275,0.000238504,0.01434119],"category_scores_gemma":[0.0032423,0.00020503221,0.00077352946,0.00006589615,0.00018299159,0.00007811727,0.00046944298,0.0012791294,0.0001466328],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00016210222,0.00042016778,0.00055480277,0.00009517679,0.0012723157,0.000069751244,0.0012450368,0.000018617491,0.00007776094,0.96525437,0.030411037,0.0004188417],"study_design_scores_gemma":[0.0002751094,0.000036300644,0.00037639344,0.00091401226,0.00014936073,0.00012719739,0.00040487334,0.00021155045,0.00032458061,0.99562514,0.001362542,0.00019296508],"about_ca_topic_score_codex":0.000005013905,"about_ca_topic_score_gemma":0.0000021693272,"teacher_disagreement_score":0.1783113,"about_ca_system_score_codex":0.00010767512,"about_ca_system_score_gemma":0.00017795991,"threshold_uncertainty_score":0.9865598},"labels":[],"label_agreement":null},{"id":"W2997853679","doi":"10.1142/s1793042120500633","title":"The p-adic Coates–Sinnott Conjecture over maximal orders","year":2019,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"McMaster University","funders":"","keywords":"Mathematics; Abelian group; Conjecture; Order (exchange); Ring of integers; Algebraic number field; Degree (music); Prime (order theory); Combinatorics; Group (periodic table); Field (mathematics); Pure mathematics; Physics","score_opus":0.011480746820612687,"score_gpt":0.296670073359906,"score_spread":0.2851893265392933,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2997853679","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.96072835,0.00018835816,0.0017720293,0.0015327175,0.0040912996,0.00015279156,0.000045502507,0.000032071825,0.03145686],"genre_scores_gemma":[0.9905606,0.00003734252,0.0004953193,0.0007294437,0.0006723802,0.000002680983,0.0000058841274,0.000036408062,0.0074599427],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99792975,0.00024671436,0.00061313104,0.00014699942,0.0008064723,0.0002569212],"domain_scores_gemma":[0.9952903,0.003222564,0.0006682541,0.00027370232,0.0004558719,0.00008935671],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0018988014,0.00019593257,0.00027111196,0.0001053111,0.00010045134,0.00012053743,0.0010017933,0.00011476452,0.015564397],"category_scores_gemma":[0.0009556877,0.00012604996,0.00028292497,0.00014144466,0.00018383714,0.00027557043,0.00012306799,0.0005347669,0.0005372414],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0010840966,0.00016211544,0.004595656,0.000016500033,0.00097396394,0.00012703518,0.0005688554,0.000013277811,0.00036622037,0.94582117,0.04072601,0.005545119],"study_design_scores_gemma":[0.0011893233,0.00006680973,0.0010934065,0.000099763114,0.000047978752,0.0011047968,0.00059185835,0.0000129191685,0.0006676833,0.8874879,0.10747097,0.0001665951],"about_ca_topic_score_codex":0.0000031719112,"about_ca_topic_score_gemma":0.0000019889092,"teacher_disagreement_score":0.06674496,"about_ca_system_score_codex":0.00010623408,"about_ca_system_score_gemma":0.0001147276,"threshold_uncertainty_score":0.9853355},"labels":[],"label_agreement":null},{"id":"W3008403333","doi":"10.1142/s1793042120500736","title":"The smallest invariant factor of the multiplicative group","year":2020,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia; University of Toronto","funders":"","keywords":"Mathematics; Multiplicative function; Asymptotic formula; Multiplicative group; Invariant (physics); Prime factor; Coprime integers; Combinatorics; Moduli; Pure mathematics; Discrete mathematics; Prime (order theory); Mathematical analysis","score_opus":0.07310333011707912,"score_gpt":0.3580763166669346,"score_spread":0.2849729865498555,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W3008403333","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8363826,0.00034615674,0.055082902,0.049880393,0.0025627913,0.0011319305,0.0006573204,0.000059747243,0.053896148],"genre_scores_gemma":[0.9973193,0.000027649396,0.0010175304,0.0004145673,0.00041292544,0.000004419457,0.0000011076563,0.000022533766,0.0007800006],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9975255,0.00053335115,0.00066979526,0.00011708102,0.0009882472,0.00016603782],"domain_scores_gemma":[0.9933599,0.0046401927,0.00083801633,0.00026665043,0.0007832783,0.00011195603],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0012930022,0.00012928412,0.00022942305,0.000031940483,0.00009926822,0.000055710112,0.002008184,0.000052995278,0.0019682485],"category_scores_gemma":[0.005040908,0.00006596436,0.0003141119,0.00014532174,0.0003640548,0.00010569083,0.00036088735,0.00047904634,0.000053979926],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0009123346,0.00017850679,0.0048305695,0.000017292503,0.0011817961,0.000038794024,0.003671965,0.0000059267204,0.002294269,0.9735788,0.010092352,0.0031973987],"study_design_scores_gemma":[0.0012349352,0.000087299464,0.0046818126,0.00017008198,0.00007327098,0.00025139996,0.0026378122,0.00026432387,0.0033810856,0.9741364,0.012922922,0.00015864403],"about_ca_topic_score_codex":0.0000052497107,"about_ca_topic_score_gemma":0.00000851402,"teacher_disagreement_score":0.16093665,"about_ca_system_score_codex":0.00008689998,"about_ca_system_score_gemma":0.0001298322,"threshold_uncertainty_score":0.9989441},"labels":[],"label_agreement":null},{"id":"W3010932436","doi":"10.1142/s1793042120500852","title":"Nevanlinna theory and algebraic values of certain meromorphic functions","year":2020,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Meromorphic and Entire Functions","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Fields Institute for Research in Mathematical Sciences","funders":"National Research Foundation; Fields Institute for Research in Mathematical Sciences","keywords":"Meromorphic function; Mathematics; Algebraic number; Exponent; Algebraic function; Pure mathematics; Algebraic cycle; Function field of an algebraic variety; Algebra over a field; Mathematical analysis","score_opus":0.04893028542954252,"score_gpt":0.3164232726491746,"score_spread":0.26749298721963205,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W3010932436","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8339722,0.00048249433,0.14351429,0.0060962187,0.0023998604,0.00018119361,0.00030200646,0.0000634616,0.012988275],"genre_scores_gemma":[0.99419135,0.00006523832,0.0022611131,0.00062605075,0.0006429219,0.0000028152467,0.000012934015,0.000026372145,0.0021711828],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9983153,0.0003560487,0.0006120183,0.0001246468,0.00047595205,0.0001160825],"domain_scores_gemma":[0.9968663,0.0018688177,0.0005200758,0.00011568702,0.00048802237,0.0001411155],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0011638792,0.00013422356,0.0002846405,0.00009798996,0.000055595112,0.00002800255,0.00031059678,0.000066574896,0.0072412076],"category_scores_gemma":[0.0021020737,0.00010998558,0.00018381132,0.000110833076,0.00017977653,0.00019894264,0.000080729376,0.00027181648,0.00005857706],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0012218268,0.00032375383,0.0019750176,0.000062605985,0.001575944,0.00008867133,0.00317719,0.000024411775,0.002118302,0.9273713,0.053447567,0.008613407],"study_design_scores_gemma":[0.0009674236,0.00016639168,0.0007408556,0.00015968872,0.00025181976,0.0005659256,0.0020930197,0.00009996592,0.00054419285,0.9839813,0.010277452,0.00015193687],"about_ca_topic_score_codex":0.0000026565835,"about_ca_topic_score_gemma":9.515668e-7,"teacher_disagreement_score":0.16021918,"about_ca_system_score_codex":0.000027447866,"about_ca_system_score_gemma":0.000078245655,"threshold_uncertainty_score":0.9936663},"labels":[],"label_agreement":null},{"id":"W3043290813","doi":"10.1142/s1793042121500780","title":"Counting multiplicative groups with prescribed subgroups","year":2021,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia; Kelowna General Hospital","funders":"","keywords":"Mathematics; Multiplicative function; Combinatorics; Prime factor; Coprime integers; Multiplicative group; Abelian group; Prime power; Group (periodic table); Prime (order theory); Additive group; Number theory; Prime number; Cyclic group; Discrete mathematics; Function (biology); Physics; Mathematical analysis","score_opus":0.04816835291095123,"score_gpt":0.3634522436880479,"score_spread":0.3152838907770967,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W3043290813","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.81567174,0.00051365735,0.14543842,0.0015040498,0.0024374684,0.00075611606,0.0004556669,0.0001230536,0.033099826],"genre_scores_gemma":[0.96959156,0.00008394155,0.025625352,0.00023572093,0.0014641526,0.00003762484,0.000095005336,0.0001374636,0.0027291765],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99478227,0.0008351346,0.00122133,0.0004815797,0.0022774716,0.0004022035],"domain_scores_gemma":[0.9891905,0.0036179803,0.0020351056,0.00066884106,0.004272385,0.00021519452],"candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0031642783,0.00046449908,0.000865803,0.00028282584,0.00007881391,0.00041810135,0.002199763,0.00030256162,0.0058459872],"category_scores_gemma":[0.0028268322,0.00037022837,0.00053553935,0.00016637021,0.00034874526,0.00038181216,0.0012762485,0.002150067,0.000058640337],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.010941171,0.0052163,0.030225731,0.0013470928,0.037984245,0.011757984,0.035770666,0.0007514661,0.0015867188,0.80330646,0.04760001,0.013512172],"study_design_scores_gemma":[0.0023741021,0.00010051543,0.0011545827,0.0035809963,0.0005454965,0.0028273498,0.00555057,0.0005092973,0.0013622396,0.97839254,0.0028093487,0.00079296395],"about_ca_topic_score_codex":0.000024112336,"about_ca_topic_score_gemma":0.0000270298,"teacher_disagreement_score":0.1750861,"about_ca_system_score_codex":0.0005603808,"about_ca_system_score_gemma":0.0007105,"threshold_uncertainty_score":0.99987495},"labels":[],"label_agreement":null},{"id":"W3083862017","doi":"10.1142/s1793042122501019","title":"Polar harmonic Maaß forms and holomorphic projection","year":2022,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Manitoba","funders":"Pacific Institute for the Mathematical Sciences","keywords":"Mathematics; Holomorphic function; Divisor (algebraic geometry); Meromorphic function; Modular form; Pure mathematics; Eisenstein series; Projection (relational algebra); Algebra over a field; Combinatorics","score_opus":0.03299611970926565,"score_gpt":0.33920011924796345,"score_spread":0.3062039995386978,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W3083862017","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9610873,0.00027055226,0.021103464,0.0011843485,0.0016091921,0.00023031107,0.0001650981,0.000060979964,0.014288783],"genre_scores_gemma":[0.9885735,0.000037811667,0.0064474074,0.00016256123,0.00021599756,0.000016277198,0.000005254575,0.000027909262,0.0045132777],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9986857,0.00011754807,0.00040129782,0.00008693089,0.00059579225,0.000112730835],"domain_scores_gemma":[0.9986588,0.00057909597,0.00041679395,0.00008940805,0.00020865463,0.000047292862],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00087638426,0.000092268514,0.00016761014,0.0001292248,0.00009896384,0.0000479869,0.00030981272,0.000023939514,0.003680931],"category_scores_gemma":[0.000609174,0.000078463934,0.00009689147,0.00006395447,0.00007462866,0.00034753088,0.00019755853,0.00032174846,0.000016531203],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00031578686,0.00032171851,0.000595802,0.000041362902,0.00036442824,0.00021033022,0.0014052407,0.000009629932,0.0007868616,0.98501414,0.008374185,0.0025604952],"study_design_scores_gemma":[0.00046303976,0.00006785919,0.00015090882,0.000040487088,0.00003399845,0.0031229937,0.0013693684,0.000036544847,0.00033819996,0.9886749,0.0056165205,0.00008520619],"about_ca_topic_score_codex":0.000002045302,"about_ca_topic_score_gemma":0.0000011369427,"teacher_disagreement_score":0.027486233,"about_ca_system_score_codex":0.00017016189,"about_ca_system_score_gemma":0.000046098412,"threshold_uncertainty_score":0.9972298},"labels":[],"label_agreement":null},{"id":"W3090503505","doi":"10.1142/s1793042121500378","title":"Conjugates of Pisot numbers","year":2020,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Waterloo","funders":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","keywords":"Conjecture; Parameterized complexity; Conjugate; Dimension (graph theory); abc conjecture; Reciprocal; Lonely runner conjecture","score_opus":0.037473671484675015,"score_gpt":0.32157194297755415,"score_spread":0.28409827149287914,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W3090503505","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9064403,0.00018746332,0.017235193,0.004001788,0.0017887433,0.00013944882,0.00016757548,0.00005541002,0.06998404],"genre_scores_gemma":[0.9938565,0.000025269013,0.0040548122,0.0009236233,0.0006322153,0.000001176815,0.000004527637,0.000025409789,0.00047649108],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9981615,0.00019970162,0.00076140836,0.00011499796,0.0006228482,0.00013953647],"domain_scores_gemma":[0.99673414,0.0015790749,0.00081942463,0.00012241743,0.00060017017,0.00014478658],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008740673,0.00014449256,0.00035127366,0.00008111591,0.00002378264,0.000022661083,0.000734579,0.00007334877,0.011805806],"category_scores_gemma":[0.0022060766,0.00012248797,0.0002806909,0.00013980977,0.00015966386,0.00024548548,0.00009918497,0.0002740719,0.00013223884],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0015939545,0.00034236445,0.004209085,0.00007774978,0.00139473,0.0002020207,0.003890147,0.000015228069,0.0022531736,0.94422424,0.037299104,0.004498218],"study_design_scores_gemma":[0.0011287562,0.00011325076,0.00025838226,0.00015233872,0.00008199029,0.00044558285,0.001463381,0.000014640541,0.012077943,0.97124004,0.012861249,0.00016246193],"about_ca_topic_score_codex":0.0000020422672,"about_ca_topic_score_gemma":3.2932022e-7,"teacher_disagreement_score":0.08741614,"about_ca_system_score_codex":0.000035499655,"about_ca_system_score_gemma":0.00007551763,"threshold_uncertainty_score":0.98909754},"labels":[],"label_agreement":null},{"id":"W3096477671","doi":"10.1142/s1793042123500355","title":"On a result of Koecher concerning Markov–Apéry-type formulas for the Riemann zeta function","year":2022,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Dalhousie University","funders":"","keywords":"Mathematics; Riemann zeta function; Riemann hypothesis; Type (biology); Euler's formula; Markov chain; Pure mathematics; Arithmetic zeta function; Proof of the Euler product formula for the Riemann zeta function; Function (biology); Prime zeta function; Mathematical analysis","score_opus":0.06011981792493461,"score_gpt":0.37039353538698533,"score_spread":0.31027371746205074,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W3096477671","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.29321128,0.00078909425,0.5951503,0.0042392816,0.013535928,0.0016672452,0.00081607647,0.00012780073,0.09046297],"genre_scores_gemma":[0.9765474,0.000019688714,0.009396602,0.00036008944,0.00046371587,0.000037233604,0.0000102075755,0.00004756653,0.013117459],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9982576,0.00014214798,0.00060917856,0.00009520055,0.0007717458,0.00012417264],"domain_scores_gemma":[0.9919855,0.0063195033,0.0008403009,0.0001699417,0.00065279636,0.000031951],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0016401053,0.00011087522,0.00022093543,0.000087090906,0.00012421142,0.000029683972,0.000546475,0.000032591866,0.0038339235],"category_scores_gemma":[0.0032540446,0.00007888454,0.00021975087,0.0000814444,0.00008784469,0.00018099375,0.000111839654,0.00031020906,0.000011473003],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0024983143,0.00019724733,0.000020399777,0.00003629442,0.00057457224,0.000012557425,0.0009332097,0.00040107654,0.0004986823,0.9659215,0.027567599,0.0013385151],"study_design_scores_gemma":[0.00084476406,0.00023024468,0.000028465145,0.00009854971,0.000105724925,0.00013570779,0.0015556392,0.0002735346,0.0005091696,0.98277926,0.013359052,0.00007991069],"about_ca_topic_score_codex":0.0000018445029,"about_ca_topic_score_gemma":0.0000015495469,"teacher_disagreement_score":0.68333614,"about_ca_system_score_codex":0.00015790723,"about_ca_system_score_gemma":0.00006376879,"threshold_uncertainty_score":0.9970767},"labels":[],"label_agreement":null},{"id":"W3134447495","doi":"10.1142/s1793042121500603","title":"A note on values of the Dedekind zeta-function at odd positive integers","year":2021,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Dedekind cut; Transcendental number; Conjecture; Integer (computer science); Irrational number; Algebraic number; Rational number; Field (mathematics); Combinatorics; Function field; Dedekind sum; Quadratic field; Transcendental function; Algebraic number field; Function (biology); Riemann zeta function; Pure mathematics; Quadratic equation; Quadratic function; Mathematical analysis","score_opus":0.018803258289416386,"score_gpt":0.30657356737980523,"score_spread":0.28777030909038886,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W3134447495","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9468898,0.00008810406,0.0065812953,0.0014343869,0.0033616712,0.00009080587,0.00010560837,0.000013718856,0.0414346],"genre_scores_gemma":[0.9925118,0.000014691513,0.00070364395,0.0007252885,0.00041406942,0.0000016468636,0.0000070121796,0.000022471562,0.0055993553],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99778426,0.0005280622,0.0005828711,0.00014336334,0.00082245085,0.00013897987],"domain_scores_gemma":[0.9955116,0.0024744323,0.00077207544,0.00024318439,0.00093792606,0.00006077323],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0011190954,0.00015706342,0.0002714997,0.00009907686,0.00008077583,0.000027449614,0.0005016426,0.00009487158,0.0051862174],"category_scores_gemma":[0.0021018893,0.00010751009,0.00043839336,0.0001686608,0.0001657678,0.00016282272,0.00018471778,0.00037165772,0.00007898533],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0038767566,0.00097119657,0.0022075586,0.00004069641,0.0025149465,0.00028474553,0.004204504,0.000081785685,0.008213487,0.94944936,0.018275807,0.009879184],"study_design_scores_gemma":[0.0007696858,0.0000870346,0.0030047782,0.000438868,0.00016497422,0.0011058056,0.0008114796,0.000009594706,0.06963179,0.9214382,0.0024115546,0.00012623491],"about_ca_topic_score_codex":0.0000017548932,"about_ca_topic_score_gemma":0.0000032979665,"teacher_disagreement_score":0.061418306,"about_ca_system_score_codex":0.00021845521,"about_ca_system_score_gemma":0.00012462196,"threshold_uncertainty_score":0.9957232},"labels":[],"label_agreement":null},{"id":"W3199313190","doi":"10.1142/s179304212250021x","title":"Hankel determinants of sequences related to Bernoulli and Euler polynomials","year":2021,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Bernoulli polynomials; Bernoulli's principle; Euler's formula; Bernoulli number; Bernoulli process; Orthogonal polynomials; Pure mathematics; Classical orthogonal polynomials; Mathematical analysis; Physics","score_opus":0.03289203413319285,"score_gpt":0.37886208300522856,"score_spread":0.3459700488720357,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W3199313190","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9913865,0.0001174459,0.0020458787,0.000316253,0.00065666233,0.000052431675,0.000054069154,0.000009507105,0.0053612627],"genre_scores_gemma":[0.96318054,0.00006259833,0.029986551,0.000109007386,0.00012281543,0.0000026201749,0.0000014870735,0.00002345082,0.006510948],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9985132,0.00011110405,0.0007253859,0.00010098044,0.00043998045,0.00010932792],"domain_scores_gemma":[0.99697375,0.0016594748,0.00049386505,0.00011819347,0.0006719414,0.00008275348],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005975526,0.00010172586,0.000317878,0.00009089306,0.000022411397,0.000038633843,0.000273558,0.0000544021,0.0023385878],"category_scores_gemma":[0.0035935475,0.000085641164,0.00010598144,0.000071010596,0.0001133687,0.0002534518,0.00013307764,0.00012468935,0.000036779373],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0003944435,0.0006367498,0.008892132,0.00024189083,0.0011807617,0.0014353323,0.0065508815,0.000025254692,0.026566967,0.934547,0.0063143424,0.013214248],"study_design_scores_gemma":[0.00033149307,0.000035451005,0.0005809702,0.0005005269,0.00004404427,0.0013470132,0.0007463442,0.000008456364,0.024392612,0.97121257,0.000709419,0.00009110124],"about_ca_topic_score_codex":0.0000022704442,"about_ca_topic_score_gemma":0.0000062198737,"teacher_disagreement_score":0.036665574,"about_ca_system_score_codex":0.000047460428,"about_ca_system_score_gemma":0.00007518205,"threshold_uncertainty_score":0.9985734},"labels":[],"label_agreement":null},{"id":"W3206183584","doi":"10.1142/s1793042122500865","title":"On a congruence involving harmonic series and Bernoulli numbers","year":2022,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Dalhousie University","funders":"Killam Trusts","keywords":"Congruence (geometry); Mathematics; Combinatorics; Prime (order theory); Conjecture; Bernoulli number; Coprime integers; Geometry","score_opus":0.024876374378253043,"score_gpt":0.32642927498819063,"score_spread":0.3015529006099376,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W3206183584","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9704646,0.0002891332,0.0043405164,0.0016834664,0.0018992135,0.00016575541,0.00014621849,0.00005811972,0.02095296],"genre_scores_gemma":[0.9823443,0.000074965,0.009155619,0.00041098663,0.000172996,0.000016505846,0.0000032516677,0.00003527881,0.0077860784],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9984381,0.00015663716,0.00043240696,0.00011193772,0.0007263202,0.0001345627],"domain_scores_gemma":[0.9973621,0.0017881504,0.0004356189,0.00011593923,0.00023009958,0.000068137575],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.000741162,0.00011938226,0.0002098974,0.00010143407,0.00012037105,0.00006931955,0.00043701884,0.000023214592,0.005592711],"category_scores_gemma":[0.001544037,0.00010946742,0.00009758377,0.000059837967,0.00014696582,0.00039803208,0.00024055585,0.00036218463,0.000020678695],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00023018054,0.00013193101,0.00021982456,0.000020844791,0.00018820078,0.00020954468,0.0012101938,0.000030960706,0.00021208478,0.9899462,0.0072625596,0.00033746002],"study_design_scores_gemma":[0.00039286359,0.00008324032,0.00006287504,0.00010876668,0.000026383042,0.0016438371,0.002354394,0.000019065383,0.00033618836,0.9922172,0.0026470616,0.000108119035],"about_ca_topic_score_codex":0.0000034826774,"about_ca_topic_score_gemma":0.0000036589681,"teacher_disagreement_score":0.013166882,"about_ca_system_score_codex":0.0001908251,"about_ca_system_score_gemma":0.000055625693,"threshold_uncertainty_score":0.9953163},"labels":[],"label_agreement":null},{"id":"W3206798471","doi":"10.1142/s1793042123500148","title":"The Euler totient function on Lucas sequences","year":2022,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":false,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"","funders":"University of Calgary","keywords":"Euler's totient function; Fibonacci number; Mathematics; Lucas sequence; Combinatorics; Euler's formula; Diophantine equation; Number theory; Fibonacci polynomials; Lucas number; Discrete mathematics; Mathematical analysis","score_opus":0.04968691522507526,"score_gpt":0.366405080860995,"score_spread":0.3167181656359197,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W3206798471","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7320207,0.00038071585,0.01530251,0.020226918,0.02037802,0.00061170297,0.0002485768,0.00011109834,0.2107198],"genre_scores_gemma":[0.9883025,0.000019454013,0.00017304887,0.00045802252,0.0006490355,0.000018330886,0.0000041490216,0.000024272926,0.010351137],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9967506,0.0007259514,0.000491657,0.00012233795,0.0017113558,0.00019809256],"domain_scores_gemma":[0.9945729,0.004062026,0.00046828162,0.00021007027,0.00061132386,0.00007542069],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0036402487,0.00011444505,0.00014884086,0.00012133478,0.00033635233,0.00009571498,0.0010255149,0.000025490277,0.013151351],"category_scores_gemma":[0.0015770061,0.00007527086,0.00021429018,0.00013156464,0.0001442202,0.00013617911,0.0002261984,0.0005996325,0.00013407465],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0015785394,0.00024206,0.00047156456,0.0000031306906,0.0005934331,0.0001376233,0.00049280014,0.00020309396,0.0000472471,0.92001957,0.06381136,0.012399572],"study_design_scores_gemma":[0.00038869752,0.00016195717,0.00017555732,0.00002357271,0.000031581007,0.00061731634,0.0022110746,0.00006565408,0.00007990482,0.8760501,0.12011361,0.00008092749],"about_ca_topic_score_codex":0.000003509574,"about_ca_topic_score_gemma":0.0000022292788,"teacher_disagreement_score":0.25628188,"about_ca_system_score_codex":0.00049973145,"about_ca_system_score_gemma":0.00018441516,"threshold_uncertainty_score":0.98775077},"labels":[],"label_agreement":null},{"id":"W4295093710","doi":"10.1142/s1793042123500458","title":"k-Diophantine m-tuples in finite fields","year":2022,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Diophantine equation; Diophantine geometry; Diophantine set; Tuple; Prime (order theory); Square number; Diophantine approximation; Asymptotic formula; Product (mathematics); Discrete mathematics; Combinatorics","score_opus":0.0461891922232668,"score_gpt":0.3741284915785501,"score_spread":0.3279392993552833,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4295093710","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9203892,0.00020313551,0.013967034,0.003585612,0.0021841454,0.00020192265,0.00014129118,0.000038140817,0.059289567],"genre_scores_gemma":[0.9920054,0.00001895666,0.0013105576,0.00032610755,0.00034106418,0.000009442402,0.0000063260786,0.000023602843,0.0059585297],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9975182,0.0005039685,0.0006182768,0.00011900283,0.0010431175,0.00019747892],"domain_scores_gemma":[0.9963878,0.0027294108,0.0003646586,0.00016590688,0.00028545377,0.000066790664],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0029741165,0.00010926503,0.00024313056,0.00030354224,0.00005912109,0.000035680096,0.0009966431,0.00003710439,0.032453995],"category_scores_gemma":[0.001739095,0.00010029939,0.00018187797,0.00020103954,0.00006818952,0.00016100031,0.00034642458,0.00065911614,0.00005855753],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0023820898,0.0012706817,0.016614053,0.000030668838,0.00082267425,0.0032142764,0.0033610428,0.0012046912,0.00025104728,0.91426015,0.046648234,0.009940408],"study_design_scores_gemma":[0.0011748251,0.00007220565,0.0004736544,0.000059369606,0.000019160207,0.0009813386,0.0013760565,0.00033806518,0.00016613778,0.97543824,0.01977067,0.00013026886],"about_ca_topic_score_codex":0.000010428236,"about_ca_topic_score_gemma":0.000008778941,"teacher_disagreement_score":0.07161626,"about_ca_system_score_codex":0.00019084652,"about_ca_system_score_gemma":0.00013088998,"threshold_uncertainty_score":0.96843046},"labels":[],"label_agreement":null},{"id":"W4297695419","doi":"10.1142/s1793042122501081","title":"On the properties of Northcott and Narkiewicz for elliptic curves","year":2022,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":false,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"","funders":"Natural Science Foundation of Guangdong Province; Australian Research Council; Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Converse; Bounded function; Elliptic curve; Rational number; Algebraic number; Endomorphism; Algebraic number field; Field (mathematics); Property (philosophy); Pure mathematics; Combinatorics; Mathematical analysis; Geometry","score_opus":0.04399531310697456,"score_gpt":0.2948826941641387,"score_spread":0.2508873810571641,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4297695419","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9923013,0.00089021446,0.0008567975,0.0024071732,0.00067825656,0.00020322527,0.00009620965,0.000008001696,0.0025588365],"genre_scores_gemma":[0.9975725,0.0000694943,0.00025397274,0.000834782,0.00013803624,0.000023989769,0.0000023772875,0.000015856758,0.0010890244],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99861723,0.0002781657,0.0004147087,0.0000801498,0.00051433325,0.00009540178],"domain_scores_gemma":[0.9965937,0.0024728905,0.0004856438,0.00012251314,0.0002943384,0.000030887153],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002085301,0.00009467926,0.00018966231,0.00007754765,0.00010688156,0.000014457238,0.0004843606,0.000019312918,0.0023885083],"category_scores_gemma":[0.0014748845,0.00005989128,0.00014713973,0.00006814033,0.000125612,0.0000856177,0.00011631997,0.00022512893,0.0000038839157],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0010597714,0.00027162538,0.00022299758,0.00010992668,0.0005050276,0.0000110141145,0.0011054417,0.00001619182,0.0004495304,0.9804424,0.014460817,0.0013452795],"study_design_scores_gemma":[0.00047992828,0.00017261336,0.00007905587,0.0003530661,0.000065378816,0.00043048966,0.0013943934,0.000020724747,0.0023444511,0.98665184,0.007918905,0.00008918603],"about_ca_topic_score_codex":0.0000010455485,"about_ca_topic_score_gemma":3.6011104e-7,"teacher_disagreement_score":0.006541913,"about_ca_system_score_codex":0.000038872025,"about_ca_system_score_gemma":0.00004942868,"threshold_uncertainty_score":0.9985234},"labels":[],"label_agreement":null},{"id":"W4385606001","doi":"10.1142/s1793042123501233","title":"Fourier coefficients of automorphic L-functions","year":2023,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Cusp form; Modular form; Zero (linguistics); Hecke operator; Cusp (singularity); Asymptotic formula; Automorphic form; Fourier series; Prime (order theory); Modular group; Combinatorics; Pure mathematics; Mathematical analysis; Geometry","score_opus":0.06215158253351223,"score_gpt":0.38974638755158725,"score_spread":0.32759480501807503,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4385606001","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.89252174,0.00003420034,0.052618068,0.0013836598,0.0030838847,0.00020442888,0.0003523785,0.000117729054,0.049683906],"genre_scores_gemma":[0.97694695,0.00001623529,0.0014492202,0.00006675675,0.00040637955,0.000003963324,0.00001517981,0.000036091657,0.021059224],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99744654,0.0002669634,0.0006871028,0.00011573518,0.0012747811,0.00020889928],"domain_scores_gemma":[0.9956888,0.0022549226,0.00051709596,0.0002269997,0.0012045428,0.00010763919],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0027407643,0.00011746581,0.0002730275,0.0003902426,0.000048238235,0.000030661067,0.0007591736,0.000067552,0.009465006],"category_scores_gemma":[0.0027117564,0.00009817964,0.00026768842,0.00040107066,0.00020162492,0.00016345605,0.00016221627,0.00030142,0.00071909104],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000910654,0.0008366439,0.0073457393,0.000060537648,0.002302878,0.0005895811,0.0016442019,0.00026228692,0.0011536859,0.73725986,0.23498678,0.012647151],"study_design_scores_gemma":[0.0012021323,0.00007538915,0.0011328127,0.00024141771,0.000098626675,0.00050830026,0.0011147467,0.000917482,0.0006930002,0.9733996,0.020461543,0.00015494578],"about_ca_topic_score_codex":0.0000030316637,"about_ca_topic_score_gemma":0.0000013347394,"teacher_disagreement_score":0.23613974,"about_ca_system_score_codex":0.00010239857,"about_ca_system_score_gemma":0.00016270607,"threshold_uncertainty_score":0.9914405},"labels":[],"label_agreement":null},{"id":"W4385606160","doi":"10.1142/s1793042124500027","title":"Arithmetic progressions in squarefull numbers","year":2023,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Arithmetic; Conjecture; Divisor (algebraic geometry); Arithmetic progression; Variety (cybernetics); Prime factor; Prime (order theory); Property (philosophy); Number theory; Discrete mathematics; Combinatorics; Statistics","score_opus":0.06374791328409778,"score_gpt":0.4271532786118919,"score_spread":0.3634053653277941,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4385606160","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9354935,0.000059921073,0.0027311086,0.0035432908,0.0019642245,0.00032411877,0.000096266194,0.00014839003,0.055639125],"genre_scores_gemma":[0.9889868,0.00004169607,0.0028813623,0.000121466794,0.0004578768,0.000016035507,0.000012206541,0.00005140218,0.00743115],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99707043,0.0004365494,0.00078034075,0.00017107169,0.0011964312,0.00034517513],"domain_scores_gemma":[0.9960346,0.00264631,0.00038574426,0.00022732817,0.0005558161,0.0001501648],"candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0033751237,0.00016026494,0.00031388033,0.0005743318,0.000042963045,0.00007051275,0.0009811539,0.00009376881,0.0061182096],"category_scores_gemma":[0.0030476567,0.00013142785,0.00023065374,0.0005785204,0.00016325277,0.00026858947,0.00020231101,0.0005460649,0.00085329695],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0011186711,0.001047933,0.039667144,0.00007145161,0.0009985401,0.004807972,0.003739041,0.000084604595,0.00029366816,0.8213132,0.10141942,0.025438342],"study_design_scores_gemma":[0.001075879,0.000039327693,0.002170484,0.00039393504,0.000026548025,0.0006848826,0.0015733375,0.00021784748,0.00015625484,0.98493886,0.008562713,0.0001599111],"about_ca_topic_score_codex":0.0000068498907,"about_ca_topic_score_gemma":0.000013593786,"teacher_disagreement_score":0.16362567,"about_ca_system_score_codex":0.00022804263,"about_ca_system_score_gemma":0.00017713555,"threshold_uncertainty_score":0.99992466},"labels":[],"label_agreement":null},{"id":"W4385606337","doi":"10.1142/s1793042124500106","title":"Squares in recurrences using elliptic curves","year":2023,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Ottawa","funders":"","keywords":"Mathematics; Quartic function; Elliptic curve; Integer (computer science); Assertion; Prime (order theory); Bounding overwatch; Combinatorics; Supersingular elliptic curve; Computation; Pure mathematics; Algorithm","score_opus":0.13396382203734652,"score_gpt":0.45421351193578696,"score_spread":0.32024968989844044,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4385606337","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.98396266,0.00042948965,0.0023402837,0.0017863986,0.0013844356,0.00014600021,0.00005343537,0.0000499271,0.0098474],"genre_scores_gemma":[0.99456674,0.00052324834,0.0018152549,0.00016052714,0.0005182401,0.0000040815157,0.000007730232,0.00003395943,0.0023702083],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9976781,0.0004123402,0.0005735529,0.00012588632,0.00097252295,0.00023757573],"domain_scores_gemma":[0.99639183,0.0025517421,0.0003592845,0.00014364686,0.00047495496,0.000078539524],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0034324424,0.00012036191,0.00026326283,0.0004131151,0.000030640284,0.000048517784,0.0007838322,0.000051637566,0.0035210026],"category_scores_gemma":[0.0028914104,0.00010008851,0.00015814201,0.00042064366,0.00012752949,0.00029378623,0.00012813279,0.00034659312,0.0002450725],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0010996072,0.0008038638,0.05827542,0.00044032125,0.0014214687,0.003336792,0.0037101058,0.00042406272,0.00093520567,0.79334635,0.118715525,0.017491259],"study_design_scores_gemma":[0.0005059106,0.000028518307,0.0008778421,0.0016903533,0.00003170557,0.0004746059,0.0011219658,0.00089585694,0.00021663135,0.9914041,0.0026092227,0.00014329147],"about_ca_topic_score_codex":0.000007980669,"about_ca_topic_score_gemma":0.0000074108257,"teacher_disagreement_score":0.19805773,"about_ca_system_score_codex":0.00015037603,"about_ca_system_score_gemma":0.00015285768,"threshold_uncertainty_score":0.9973899},"labels":[],"label_agreement":null},{"id":"W4387641873","doi":"10.1142/s1793042124500234","title":"On the jth smallest modulus of a covering system with distinct moduli","year":2023,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université de Montréal","funders":"Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada; Courtois Foundation","keywords":"Moduli; Mathematics; Modulus; Bounded function; Constant (computer programming); Modular equation; Pure mathematics; Moduli space; Combinatorics; Mathematical analysis; Geometry; Moduli of algebraic curves; Computer science; Physics","score_opus":0.02570177866368628,"score_gpt":0.2884431693469132,"score_spread":0.26274139068322694,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4387641873","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9747901,0.000012498275,0.0072430666,0.00021405592,0.0010418843,0.00009006677,0.00008578959,0.000030393938,0.016492147],"genre_scores_gemma":[0.9988127,0.0000057043158,0.0003759714,0.00006397185,0.0002456342,0.000003981496,0.0000023334512,0.000023677536,0.0004660611],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9985124,0.0001640323,0.0004245918,0.00009455772,0.0006768733,0.00012757373],"domain_scores_gemma":[0.9968887,0.0019728588,0.0005399329,0.00021312326,0.0003417751,0.000043589538],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001096474,0.00012824032,0.00022320203,0.00011648991,0.00008239373,0.000030024168,0.00064250536,0.00004140412,0.00045076993],"category_scores_gemma":[0.0006019696,0.00006806679,0.00015662663,0.00012963258,0.00013160367,0.00006392142,0.00011147336,0.00022600687,0.000013994235],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00057459425,0.000039001465,0.0005698847,0.000033449498,0.00047543924,0.00013762951,0.00089886325,0.0005592396,0.000040569666,0.9939461,0.002273048,0.00045219492],"study_design_scores_gemma":[0.0007362599,0.000121503326,0.003251786,0.0008212127,0.00005656058,0.00069894857,0.0014627805,0.0008582262,0.00040294795,0.9910683,0.000386181,0.00013531765],"about_ca_topic_score_codex":0.0000036728918,"about_ca_topic_score_gemma":0.0000027160359,"teacher_disagreement_score":0.024022566,"about_ca_system_score_codex":0.00006963264,"about_ca_system_score_gemma":0.000036981794,"threshold_uncertainty_score":0.49356148},"labels":[],"label_agreement":null},{"id":"W4387641893","doi":"10.1142/s1793042124500246","title":"A lower bound on the proportion of modular elliptic curves over Galois CM fields","year":2023,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":false,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Galois module; Elliptic curve; Upper and lower bounds; Pure mathematics; Quadratic equation; Algebraic number field; Field (mathematics); Combinatorics; Discrete mathematics; Mathematical analysis; Geometry","score_opus":0.03080293565947499,"score_gpt":0.31936637858006384,"score_spread":0.28856344292058883,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4387641893","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9885193,0.00008029459,0.0016661885,0.0019836964,0.0012490577,0.00012494088,0.000029674426,0.000026227208,0.006320636],"genre_scores_gemma":[0.99529284,0.00014312175,0.000106613516,0.00068592647,0.00039416223,0.0000060134475,0.000007545612,0.000022307888,0.0033414776],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9978969,0.00023523437,0.0006081155,0.00011409316,0.0009906596,0.00015500833],"domain_scores_gemma":[0.9967263,0.0018685756,0.0006348436,0.00024920082,0.00047060096,0.000050475835],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0023638355,0.00013758721,0.00023312808,0.00015483914,0.00005146347,0.000029303748,0.00058666564,0.000080053665,0.0065932116],"category_scores_gemma":[0.0019912543,0.00008964653,0.00027310158,0.00022632405,0.00013510877,0.00017611415,0.00008148995,0.00033069833,0.00017578049],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0008931159,0.0005983627,0.0013719337,0.00014383177,0.0011290788,0.00024726728,0.0010418858,0.00008519465,0.0008871987,0.9121813,0.07937832,0.0020424952],"study_design_scores_gemma":[0.00039054963,0.000108306434,0.0021630286,0.0006744001,0.00006628542,0.0001680279,0.00027301395,0.000059826478,0.0033596554,0.9893419,0.003277507,0.00011751387],"about_ca_topic_score_codex":0.0000027713158,"about_ca_topic_score_gemma":7.2874536e-7,"teacher_disagreement_score":0.077160574,"about_ca_system_score_codex":0.00005272878,"about_ca_system_score_gemma":0.00006143473,"threshold_uncertainty_score":0.9943149},"labels":[],"label_agreement":null},{"id":"W4387642058","doi":"10.1142/s1793042124500362","title":"A Dirichlet series related to the error term in the Prime Number Theorem","year":2023,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Lethbridge","funders":"University of Lethbridge","keywords":"Mathematics; Dirichlet series; Riemann zeta function; Term (time); Dirichlet distribution; Analytic number theory; Modulo; Riemann hypothesis; Prime number theorem; Combinatorics; Prime (order theory); Asymptotic formula; Pure mathematics; Prime number; Mathematical analysis","score_opus":0.04793180489091054,"score_gpt":0.3973320999042588,"score_spread":0.34940029501334824,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4387642058","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.89461434,0.000035107463,0.00076287985,0.033019334,0.001324162,0.00056713336,0.00009765862,0.00008634391,0.06949303],"genre_scores_gemma":[0.9817239,0.000028606277,0.00043975684,0.0008692562,0.0004404553,0.00003326893,0.000010775228,0.000053226308,0.016400773],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9957666,0.0012528896,0.0008593479,0.00020018421,0.0015262525,0.0003947609],"domain_scores_gemma":[0.9943057,0.004195695,0.0003953812,0.000490343,0.00051232,0.00010057358],"candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0082460465,0.00021659672,0.00031032265,0.00023356863,0.00012043583,0.00017126535,0.002406074,0.000095172196,0.0059595923],"category_scores_gemma":[0.0029877685,0.00011691661,0.00027402447,0.0007240893,0.00024620185,0.00031644918,0.00033443206,0.00077826006,0.002626081],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00082369364,0.00025750446,0.007906825,0.000013869336,0.0006373026,0.000929538,0.015842484,0.00004161803,0.00012814808,0.8832252,0.08620799,0.0039858227],"study_design_scores_gemma":[0.00062137557,0.00004430429,0.006423723,0.00016774764,0.00004434155,0.002094889,0.0056468677,0.00005827298,0.00010743791,0.96108264,0.023542732,0.00016564784],"about_ca_topic_score_codex":0.0000068044988,"about_ca_topic_score_gemma":0.000022683582,"teacher_disagreement_score":0.08710953,"about_ca_system_score_codex":0.00016334042,"about_ca_system_score_gemma":0.00013904144,"threshold_uncertainty_score":0.99815047},"labels":[],"label_agreement":null},{"id":"W4392782098","doi":"10.1142/s1793042124500556","title":"Statistics for Iwasawa invariants of elliptic curves, II","year":2024,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":false,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"","funders":"Pacific Institute for the Mathematical Sciences; Simons Foundation","keywords":"Mathematics; Iwasawa theory; Elliptic curve; Pure mathematics; Supersingular elliptic curve; Intersection (aeronautics); Algebra over a field; Conjecture","score_opus":0.03337870339870977,"score_gpt":0.3512876252134634,"score_spread":0.3179089218147536,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4392782098","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.091262646,0.0042409445,0.86796474,0.002100766,0.009816672,0.000530349,0.0035403697,0.000091694266,0.020451803],"genre_scores_gemma":[0.94688344,0.00049780146,0.04062654,0.0005315879,0.0012212903,0.000012093894,0.00006222539,0.00007258607,0.010092431],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99822706,0.00013482478,0.0007951371,0.00012503075,0.0005623955,0.00015553602],"domain_scores_gemma":[0.9948771,0.0037437056,0.00043588306,0.00014587442,0.00072187494,0.000075545075],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0019867613,0.0001446674,0.00030809504,0.00018065226,0.00004062341,0.000034740264,0.0005464679,0.000070902206,0.005558525],"category_scores_gemma":[0.0022124418,0.00012029147,0.00022553568,0.00013001559,0.00010710296,0.00024935757,0.00008973628,0.00023696705,0.00004367595],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00027371326,0.00019859931,0.00005377126,0.00040755744,0.000856546,0.00008784728,0.00049858436,0.0000035172231,0.00021923306,0.893264,0.09810277,0.006033892],"study_design_scores_gemma":[0.00045061944,0.00011370232,0.00004883047,0.0014539758,0.00016354378,0.0005447069,0.00015337177,0.00009369174,0.0012616874,0.9682069,0.0273877,0.000121266006],"about_ca_topic_score_codex":0.0000013188875,"about_ca_topic_score_gemma":6.8225876e-7,"teacher_disagreement_score":0.8556208,"about_ca_system_score_codex":0.00006897781,"about_ca_system_score_gemma":0.00017368881,"threshold_uncertainty_score":0.99535054},"labels":[],"label_agreement":null},{"id":"W4395670166","doi":"10.1142/s1793042124501094","title":"A function related to the Mordell–Weil rank of elliptic curves","year":2024,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Elliptic curve; Rank (graph theory); Pure mathematics; Function (biology); Modular elliptic curve; Algebra over a field; Combinatorics; Quarter period","score_opus":0.01783951758261028,"score_gpt":0.31742592283800636,"score_spread":0.2995864052553961,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4395670166","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8211107,0.008961952,0.07307237,0.01552104,0.017499024,0.0006025263,0.00019693581,0.00017333204,0.06286212],"genre_scores_gemma":[0.99180245,0.00021972739,0.0005195223,0.0005975473,0.0004991863,0.0000055527785,0.000005925398,0.00003062633,0.0063194716],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9980142,0.00029339117,0.000731859,0.00012712281,0.0006976826,0.00013570691],"domain_scores_gemma":[0.9967252,0.002214898,0.0003061931,0.00019854638,0.00048585545,0.000069333335],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0026885113,0.00013940297,0.00023771185,0.00019451238,0.000037646387,0.000044708515,0.0006020283,0.00006794918,0.0071454295],"category_scores_gemma":[0.0011906021,0.00009055324,0.00028418942,0.0003268198,0.000087151224,0.00022771723,0.00008233339,0.00037819208,0.00036195526],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00095147936,0.00021071862,0.00012953898,0.00019004763,0.0018153826,0.00011917414,0.0019982238,0.00008988492,0.00047990837,0.87928075,0.10121991,0.013514978],"study_design_scores_gemma":[0.0003255199,0.00009184859,0.00023494386,0.0014408446,0.00020130702,0.0008360376,0.00051677314,0.000074643925,0.00063577195,0.9517691,0.04375582,0.00011734882],"about_ca_topic_score_codex":0.0000020326722,"about_ca_topic_score_gemma":7.7161144e-7,"teacher_disagreement_score":0.17069173,"about_ca_system_score_codex":0.00006207715,"about_ca_system_score_gemma":0.00008809681,"threshold_uncertainty_score":0.9937622},"labels":[],"label_agreement":null},{"id":"W4398253935","doi":"10.1142/s1793042124501203","title":"The least primary factor of the multiplicative group","year":2024,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Multiplicative function; Group (periodic table); Factor (programming language); Primary (astronomy); Multiplicative group; Pure mathematics; Combinatorics; Mathematical analysis; Chemistry","score_opus":0.03826451011217357,"score_gpt":0.3706028968932196,"score_spread":0.33233838678104605,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4398253935","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.73390293,0.003108514,0.055406798,0.017734177,0.011142161,0.0012948716,0.0011032192,0.00015868155,0.17614864],"genre_scores_gemma":[0.99101734,0.00006338647,0.00065431074,0.00010418473,0.00051847677,0.0000064580017,0.0000017869894,0.0000328218,0.00760124],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9975448,0.00044369086,0.00060945353,0.00012163224,0.0011094231,0.00017099126],"domain_scores_gemma":[0.99251527,0.006119917,0.00039395792,0.0003001166,0.0006102286,0.000060531547],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001893151,0.00012958507,0.00019971337,0.00007472593,0.00008876702,0.00010577266,0.0015478702,0.000054240707,0.0014309612],"category_scores_gemma":[0.0014925473,0.00006373124,0.00039063298,0.00016694213,0.0004332626,0.00019478622,0.00027944567,0.0005395362,0.00008117051],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00037441237,0.00016775538,0.0011030241,0.000048664107,0.0014081432,0.00004838324,0.0016518622,0.0000020687833,0.0018009099,0.9562467,0.014974425,0.022173706],"study_design_scores_gemma":[0.00034672322,0.000030127194,0.0025328193,0.00042387022,0.000060411352,0.00046755926,0.0007896668,0.000116401425,0.0011715462,0.96280354,0.03115931,0.00009802654],"about_ca_topic_score_codex":0.0000033375773,"about_ca_topic_score_gemma":0.000004427854,"teacher_disagreement_score":0.2571144,"about_ca_system_score_codex":0.00021124067,"about_ca_system_score_gemma":0.00018204581,"threshold_uncertainty_score":0.99948186},"labels":[],"label_agreement":null},{"id":"W4398253949","doi":"10.1142/s1793042124300011","title":"Unimodal sequences: From Isaac Newton to June Huh","year":2024,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Combinatorics; Algebra over a field; Applied mathematics; Pure mathematics","score_opus":0.03212411685524074,"score_gpt":0.3778363476743974,"score_spread":0.34571223081915664,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4398253949","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.51811874,0.00084096193,0.38438764,0.012531153,0.046744645,0.00048465928,0.0006087911,0.00038229526,0.035901118],"genre_scores_gemma":[0.8911738,0.000053968044,0.09304044,0.0010412118,0.0050173406,0.000014541363,0.000017302918,0.00013359847,0.009507821],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.998063,0.00011507145,0.0006671532,0.00016783761,0.00081723864,0.00016968361],"domain_scores_gemma":[0.9962378,0.0027064832,0.0002618051,0.00020275792,0.0004531125,0.0001380266],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00065611146,0.00017727254,0.00028438066,0.00016766893,0.000029503668,0.00015092132,0.0008034093,0.00007940095,0.0032614537],"category_scores_gemma":[0.0016505186,0.00014562986,0.00019765705,0.00016661432,0.000055280172,0.00039700678,0.00013294697,0.00034528927,0.0004280201],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00011993393,0.00011510267,0.00002180811,0.000022795579,0.00044395015,0.00043048864,0.0019156152,0.000040108254,0.0013148315,0.94584984,0.046189446,0.003536112],"study_design_scores_gemma":[0.00026905176,0.00003755084,0.0000087762755,0.0006337782,0.000053556618,0.0002537073,0.0004075483,0.00008976033,0.0015879171,0.92149484,0.075031795,0.00013169745],"about_ca_topic_score_codex":0.000006858389,"about_ca_topic_score_gemma":0.0000043972814,"teacher_disagreement_score":0.37305504,"about_ca_system_score_codex":0.00027756975,"about_ca_system_score_gemma":0.00014573577,"threshold_uncertainty_score":0.9976497},"labels":[],"label_agreement":null},{"id":"W4400581791","doi":"10.1142/s1793042125500101","title":"Generalized <i>L</i>-functions related to the Riemann zeta function","year":2024,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Calgary","funders":"Research Grants Council, University Grants Committee; Deutsche Forschungsgemeinschaft","keywords":"Mathematics; Riemann zeta function; Riemann hypothesis; Arithmetic zeta function; Particular values of Riemann zeta function; Riemann Xi function; Pure mathematics; Prime zeta function","score_opus":0.017451324785263636,"score_gpt":0.33338174480699473,"score_spread":0.3159304200217311,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4400581791","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.45554173,0.0016480546,0.44213745,0.022437366,0.02955145,0.00038934674,0.00025201635,0.00028794797,0.04775463],"genre_scores_gemma":[0.9663657,0.000048571153,0.0032703406,0.001486682,0.0016915274,0.000012912815,0.000019923196,0.000049645863,0.02705472],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99861974,0.00013016647,0.00048267312,0.00012706767,0.0005114658,0.00012890324],"domain_scores_gemma":[0.99831045,0.00091477076,0.00016348044,0.00016226232,0.00037421982,0.00007484216],"candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0008860929,0.00011986364,0.00014713506,0.00018177403,0.000074708165,0.000111898225,0.0003863208,0.000056397716,0.005264742],"category_scores_gemma":[0.00064495794,0.000075670214,0.00023402055,0.0002990874,0.000040021165,0.0002874475,0.00006898172,0.00035110986,0.0008149108],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00019874795,0.000062661275,0.00005764822,0.0000079027,0.0007103752,0.00008373176,0.000501121,0.00017578212,0.0002788742,0.8332444,0.15121777,0.013460992],"study_design_scores_gemma":[0.00021019598,0.00003483062,0.00010724151,0.00010532353,0.000082094506,0.0006149085,0.00021260818,0.000051205356,0.0000759658,0.7564175,0.24201263,0.000075466865],"about_ca_topic_score_codex":7.007826e-7,"about_ca_topic_score_gemma":0.0000025726245,"teacher_disagreement_score":0.51082397,"about_ca_system_score_codex":0.00008914577,"about_ca_system_score_gemma":0.000058494883,"threshold_uncertainty_score":0.99996305},"labels":[],"label_agreement":null},{"id":"W4403137057","doi":"10.1142/s1793042125500368","title":"Distribution of ω(n) over <i>h</i>-free and <i>h</i>-full numbers","year":2024,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Distribution (mathematics); Combinatorics; Mathematical analysis","score_opus":0.02394495061403664,"score_gpt":0.3540235089900219,"score_spread":0.33007855837598526,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4403137057","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.9254013,0.00091994385,0.04045276,0.0017888143,0.0022577657,0.0001947405,0.000946413,0.0000748976,0.027963402],"genre_scores_gemma":[0.9956337,0.00013167638,0.0016179762,0.00006991986,0.0004734148,0.0000026221262,0.000019167373,0.000035206634,0.0020162691],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99778736,0.00021020613,0.0006904643,0.00016074647,0.00096638926,0.00018483528],"domain_scores_gemma":[0.99659204,0.0022104357,0.000298433,0.00023617767,0.0005446091,0.00011828334],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0020313764,0.00015465205,0.00029431825,0.00014157561,0.000028324832,0.000095429474,0.00069887936,0.00008563956,0.00299672],"category_scores_gemma":[0.0015708903,0.00012582037,0.00023623361,0.00017302232,0.0002631011,0.00038721183,0.0002298756,0.00037508752,0.000038573467],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00058077986,0.00015539097,0.0010882248,0.00011752305,0.0010431557,0.00031512103,0.0005971511,0.0000026066598,0.0010310696,0.9053447,0.083030805,0.006693441],"study_design_scores_gemma":[0.0006832423,0.00006016184,0.00044029445,0.0005033559,0.00010975895,0.0013541362,0.00028353013,0.00011279084,0.00074243324,0.97125286,0.024325483,0.0001319809],"about_ca_topic_score_codex":0.000009086804,"about_ca_topic_score_gemma":0.0000052238493,"teacher_disagreement_score":0.07023249,"about_ca_system_score_codex":0.00014952714,"about_ca_system_score_gemma":0.00014490096,"threshold_uncertainty_score":0.9979147},"labels":[],"label_agreement":null},{"id":"W4406721169","doi":"10.1142/s179304212550068x","title":"Congruence relations of Ankeny–Artin–Chowla type for real quadratic fields","year":2025,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Congruence (geometry); Type (biology); Quadratic equation; Pure mathematics; Geometry","score_opus":0.024092905277696416,"score_gpt":0.35741119364173535,"score_spread":0.33331828836403893,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4406721169","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.86903894,0.00010394425,0.07455388,0.0013738353,0.0028805977,0.0002302013,0.000082057624,0.000027867125,0.051708676],"genre_scores_gemma":[0.9860815,0.000026049998,0.005812906,0.00020679049,0.00020843204,0.000005362366,0.000009290465,0.000011634301,0.007638082],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99862486,0.00014473453,0.00070954766,0.00010118528,0.000296637,0.00012301096],"domain_scores_gemma":[0.9944468,0.0036746985,0.0005658362,0.00016834159,0.0010984666,0.00004584782],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0010294397,0.00010939752,0.00025901967,0.00017067611,0.000050685583,0.000022543021,0.000485422,0.00009240368,0.0018727402],"category_scores_gemma":[0.0033391116,0.00009563229,0.00018993196,0.00019743216,0.000109891655,0.00019402141,0.000054623084,0.00020921334,0.000020793246],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00073754875,0.00021985105,0.005070573,0.000051652692,0.00058905745,0.000013033596,0.00070540904,0.00003289152,0.00022755648,0.95837235,0.03164537,0.0023346827],"study_design_scores_gemma":[0.0007095468,0.00007457964,0.0020295815,0.00022985875,0.00010656399,0.000060319577,0.000435716,0.000053606313,0.0013212096,0.99095577,0.0039337273,0.00008954072],"about_ca_topic_score_codex":0.0000057577477,"about_ca_topic_score_gemma":0.000008472651,"teacher_disagreement_score":0.117042504,"about_ca_system_score_codex":0.000062205836,"about_ca_system_score_gemma":0.00018085999,"threshold_uncertainty_score":0.9990397},"labels":[],"label_agreement":null},{"id":"W4406721350","doi":"10.1142/s1793042125500654","title":"The classification of the refined Humbert invariant for curves of genus 2","year":2025,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Invariant (physics); Genus; Pure mathematics; Combinatorics; Botany; Mathematical physics; Biology","score_opus":0.03185593349748178,"score_gpt":0.3427204787538217,"score_spread":0.31086454525633994,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4406721350","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.78644973,0.0029849473,0.073411815,0.03090714,0.009995724,0.0014011943,0.000513013,0.000040348972,0.09429607],"genre_scores_gemma":[0.99374014,0.00014601478,0.0010850916,0.00038304707,0.0001670025,0.000013064834,0.000004073877,0.000012911935,0.004448625],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9981917,0.00030437412,0.000859461,0.0000858583,0.00045124214,0.000107342734],"domain_scores_gemma":[0.9924348,0.00498379,0.0011880358,0.0003009637,0.0010691185,0.000023293356],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0027431082,0.000101894744,0.00023588758,0.00007611497,0.00008665772,0.000016843667,0.0010611418,0.00006366316,0.00027279631],"category_scores_gemma":[0.004811493,0.00005768909,0.0003166786,0.00018311254,0.0002343046,0.00010062388,0.00010738082,0.00018255824,0.000002549032],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0005611727,0.00015971901,0.0006314557,0.00010239929,0.0006100881,0.0000010785064,0.0002104224,0.0000023358255,0.0014761747,0.96443856,0.026682263,0.005124355],"study_design_scores_gemma":[0.0006271882,0.000028516302,0.005311641,0.0007834453,0.00012958498,0.000054126787,0.00043622425,0.000023438546,0.0069815773,0.96628094,0.019283276,0.00006003331],"about_ca_topic_score_codex":0.0000030214337,"about_ca_topic_score_gemma":0.000005337571,"teacher_disagreement_score":0.20729041,"about_ca_system_score_codex":0.00005538994,"about_ca_system_score_gemma":0.00017953929,"threshold_uncertainty_score":0.5760154},"labels":[],"label_agreement":null},{"id":"W4407238997","doi":"10.1142/s1793042125500691","title":"Multiplicative groups avoiding a fixed group","year":2025,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia; Vancouver Island University","funders":"","keywords":"Mathematics; Group (periodic table); Multiplicative group; Multiplicative function; Fixed point; Pure mathematics; Combinatorics; Mathematical analysis","score_opus":0.042543022919102065,"score_gpt":0.4004587122845852,"score_spread":0.3579156893654831,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4407238997","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.64818877,0.00025010257,0.20464708,0.0028497777,0.003344217,0.00047059183,0.00017312991,0.00012284712,0.13995348],"genre_scores_gemma":[0.98760563,0.000025422134,0.008059239,0.0003624618,0.00040545355,0.000014966626,0.00000769273,0.00002743738,0.003491684],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99757767,0.0006711294,0.000665408,0.00016926721,0.00069178874,0.00022473425],"domain_scores_gemma":[0.9914575,0.0069345417,0.00043744218,0.00023994813,0.0008470186,0.00008350089],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0031854853,0.00016123547,0.00028651778,0.0003576195,0.00009464833,0.00009118886,0.001135698,0.00009143273,0.0026142525],"category_scores_gemma":[0.005599131,0.00013675721,0.00025454498,0.00023291117,0.0001560041,0.000301911,0.00025408028,0.00067911035,0.00012478742],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0008051199,0.00032111228,0.0013338998,0.000024425894,0.00070804346,0.00010682988,0.0010885529,0.0000024724852,0.0024367042,0.97246486,0.0129993465,0.007708605],"study_design_scores_gemma":[0.0011751319,0.00004127528,0.0008580482,0.00034205994,0.00003828838,0.00020557996,0.0012339671,0.00008232774,0.0014264191,0.98559064,0.00888349,0.00012274808],"about_ca_topic_score_codex":0.0000025739253,"about_ca_topic_score_gemma":0.0000030867388,"teacher_disagreement_score":0.33941686,"about_ca_system_score_codex":0.00026858816,"about_ca_system_score_gemma":0.000093112,"threshold_uncertainty_score":0.9982975},"labels":[],"label_agreement":null},{"id":"W4407265282","doi":"10.1142/s179304212550071x","title":"On the index of friability","year":2025,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Control Systems Optimization","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Université Laval","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Friability; Mathematics; Index (typography); Statistics; Mathematical economics; Computer science; Medicine; Pharmacology","score_opus":0.0031413528907548055,"score_gpt":0.23842891819201864,"score_spread":0.23528756530126382,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4407265282","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.14918025,0.00016345952,0.75275666,0.00090171176,0.0036336442,0.0001496163,0.000043502907,0.00003896444,0.093132176],"genre_scores_gemma":[0.9993536,0.000008762039,0.00023206079,0.00011038561,0.00009356455,0.000002531049,9.0274546e-7,0.000006007315,0.00019221037],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99933046,0.000067465415,0.00031402265,0.00003556576,0.0002049151,0.00004754039],"domain_scores_gemma":[0.9986747,0.0008095331,0.00012492808,0.00009758533,0.00028067298,0.000012561382],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00044235404,0.00005422762,0.00010287939,0.000065700384,0.000010556868,0.000010619467,0.00029114293,0.000030122828,0.0004910959],"category_scores_gemma":[0.0004892172,0.000037394213,0.00007152446,0.00006647607,0.000030284484,0.00008530238,0.00001585136,0.00013474113,0.000007348144],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00033488765,0.000068138244,0.0028436615,0.000018709954,0.00068271963,0.000007450294,0.00021442371,0.44457924,0.0012106784,0.5315127,0.0061684153,0.012358977],"study_design_scores_gemma":[0.0014300296,0.00003324062,0.0058642942,0.0005651442,0.000037377016,0.000046247933,0.0002860782,0.032256287,0.0037724695,0.9454612,0.010101166,0.00014646952],"about_ca_topic_score_codex":9.619365e-7,"about_ca_topic_score_gemma":6.2682597e-7,"teacher_disagreement_score":0.8501733,"about_ca_system_score_codex":0.00009007849,"about_ca_system_score_gemma":0.00002125342,"threshold_uncertainty_score":0.53771555},"labels":[],"label_agreement":null},{"id":"W4411515085","doi":"10.1142/s1793042125501088","title":"Matsuda monoids and Artin’s primitive root conjecture","year":2025,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Conjecture; Root (linguistics); Pure mathematics; Artin L-function; Primitive root modulo n; Combinatorics; Modulo; Conductor; Geometry","score_opus":0.014434376623161793,"score_gpt":0.3097474703166745,"score_spread":0.2953130936935127,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4411515085","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.95078593,0.00021325883,0.009329687,0.0020428232,0.0010571192,0.000073091265,0.000029851122,0.000021572285,0.036446687],"genre_scores_gemma":[0.9925248,0.00003065637,0.0023959777,0.00044366185,0.00035938874,0.0000025582735,0.000002169632,0.000013370042,0.004227426],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99902207,0.00008907851,0.00039327453,0.000106134,0.00027819996,0.00011124336],"domain_scores_gemma":[0.9985359,0.0007170019,0.0002940375,0.0000943157,0.00030697888,0.000051821295],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00048372117,0.00011609487,0.0002031375,0.00011970217,0.000038658538,0.000074167576,0.00028245166,0.00006421739,0.0011072576],"category_scores_gemma":[0.0005908351,0.0000932551,0.0001086066,0.000047556685,0.00008831271,0.00016846744,0.000079861864,0.00024818568,0.000020981739],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00020497145,0.00015510003,0.0041543166,0.000024901548,0.0005556888,0.00009970176,0.0007554635,0.0000038740163,0.0004431437,0.9613324,0.021246845,0.011023627],"study_design_scores_gemma":[0.0006916952,0.000028103956,0.0071272627,0.00027732586,0.000053238506,0.00034304432,0.00031612423,0.000014735585,0.002568516,0.9771965,0.011286621,0.00009682273],"about_ca_topic_score_codex":0.000002417923,"about_ca_topic_score_gemma":0.000004960859,"teacher_disagreement_score":0.041738883,"about_ca_system_score_codex":0.00006704873,"about_ca_system_score_gemma":0.00007020214,"threshold_uncertainty_score":0.99980587},"labels":[],"label_agreement":null},{"id":"W4413087783","doi":"10.1142/s1793042126500041","title":"An improved lower bound on the image of the 2-adic character map for the Heisenberg algebra via modular linear differential equations","year":2025,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"advanced mathematical theories","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"McMaster University","funders":"","keywords":"Mathematics; Character (mathematics); Algebra over a field; Modular design; Heisenberg group; Pure mathematics; Image (mathematics); Differential (mechanical device); Geometry; Physics; Computer science","score_opus":0.021164262011321308,"score_gpt":0.34403369768207803,"score_spread":0.3228694356707567,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4413087783","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.10909896,0.000036723508,0.8809469,0.005893191,0.0024198862,0.0005782534,0.00016271013,0.000018750867,0.00084461924],"genre_scores_gemma":[0.9921133,0.0000072729304,0.004310195,0.0006726881,0.00066290464,0.000046635156,0.000005279395,0.000036247693,0.0021454662],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.998239,0.00025307894,0.00068922236,0.000133955,0.0005115262,0.00017321383],"domain_scores_gemma":[0.99061894,0.0074232155,0.00067141006,0.0005227241,0.0007237661,0.00003994946],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0010693113,0.00018598425,0.00026662947,0.000062234845,0.00019150361,0.00008424749,0.0012898693,0.000069800175,0.0011165629],"category_scores_gemma":[0.0026936608,0.00008651756,0.00040693927,0.000092192204,0.00038544126,0.0002288956,0.00013392662,0.0003667586,0.000013626616],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00051509356,0.00043592817,0.0000068776876,0.000030047539,0.0006342366,0.000002230171,0.00049294584,0.000027839407,0.011866499,0.9841255,0.0008206613,0.0010421573],"study_design_scores_gemma":[0.0005655202,0.000059686758,0.000088893095,0.00020272133,0.00016077881,0.00001639272,0.00029808775,0.0046829954,0.009045549,0.9832003,0.001588639,0.00009043766],"about_ca_topic_score_codex":0.0000011716171,"about_ca_topic_score_gemma":0.0000022981505,"teacher_disagreement_score":0.8830143,"about_ca_system_score_codex":0.00008118823,"about_ca_system_score_gemma":0.00008238584,"threshold_uncertainty_score":0.99979657},"labels":[],"label_agreement":null},{"id":"W4416454070","doi":"10.1142/s1793042126500338","title":"On level 2 modular differential equations","year":2025,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic and geometric function theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Ottawa","funders":"","keywords":"Modular design; Modular form; Modular curve; Modular group; Meromorphic function; Modular elliptic curve; Equivariant map; Eisenstein series; Modular invariance","score_opus":0.04603593282377197,"score_gpt":0.35293815295853287,"score_spread":0.3069022201347609,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4416454070","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.04144368,0.00003311152,0.91060144,0.0006662751,0.0024429616,0.000049770668,0.000058911595,0.000019028921,0.04468484],"genre_scores_gemma":[0.95980275,0.000008729987,0.0010681576,0.00052826764,0.00034452556,0.0000024456906,0.0000071937884,0.000010702728,0.038227204],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9986909,0.00012128184,0.0004688027,0.00009756871,0.00051725004,0.000104199],"domain_scores_gemma":[0.996192,0.002748326,0.00031468412,0.00014610156,0.0005502991,0.00004863538],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0006004546,0.00010857948,0.00019006686,0.00043490677,0.00005280936,0.000041847365,0.00042405308,0.00006297657,0.010540734],"category_scores_gemma":[0.0035208291,0.00008658009,0.0002310376,0.00020342409,0.00006200914,0.00010699304,0.000055474306,0.0002329471,0.00014112452],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00026962176,0.00025734046,0.000092365204,0.000005007092,0.00059044897,0.000019963365,0.000077582175,0.000075347,0.000042360414,0.95433944,0.03880083,0.0054296614],"study_design_scores_gemma":[0.00074498035,0.00003291186,0.0005026712,0.00010877685,0.000081476406,0.000031728123,0.00015479822,0.00034827413,0.00019790209,0.99233675,0.0053839497,0.000075773714],"about_ca_topic_score_codex":0.0000014291504,"about_ca_topic_score_gemma":4.2519358e-7,"teacher_disagreement_score":0.9183591,"about_ca_system_score_codex":0.0001274338,"about_ca_system_score_gemma":0.00009014569,"threshold_uncertainty_score":0.9903638},"labels":[],"label_agreement":null},{"id":"W4417246034","doi":"10.1142/s1793042126500521","title":"Higher Euler–Kronecker constants of number fields","year":2025,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs","keywords":"Laurent series; Dedekind cut; Algebraic number field; Logarithm; Dedekind eta function; Dedekind sum; Riemann zeta function; Field (mathematics); Constant (computer programming)","score_opus":0.029936519774211183,"score_gpt":0.3768875682345834,"score_spread":0.3469510484603722,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4417246034","genre_codex":"other","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"codex-gemma-dda1882f352a","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.17098899,0.00025955628,0.11103083,0.0013420276,0.005772494,0.00018404308,0.00011145717,0.000042880434,0.7102677],"genre_scores_gemma":[0.9507951,0.000066499146,0.018368807,0.00023119706,0.00024198736,0.0000036306724,0.0000021670585,0.000021314205,0.030269291],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99831367,0.00009989106,0.0008067864,0.00009880116,0.0005428603,0.00013802134],"domain_scores_gemma":[0.99606705,0.0023784447,0.0005574854,0.00017919895,0.00076837605,0.000049456],"candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00054127583,0.00013390974,0.0003472016,0.00010922885,0.000023274362,0.000031789208,0.0005142451,0.000092847484,0.017157793],"category_scores_gemma":[0.0015151124,0.00011126462,0.00020811713,0.00009497232,0.00018373891,0.00031101628,0.00012569701,0.00025260187,0.00010673776],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00016127374,0.00024079952,0.0009931383,0.000058930018,0.00046582596,0.000056268615,0.0002452154,0.0000051936345,0.0001437836,0.9709369,0.025561554,0.0011311178],"study_design_scores_gemma":[0.00064495526,0.000012833212,0.00029608607,0.0005672149,0.00006987532,0.00011456507,0.00024765808,0.0000074107234,0.0018397941,0.98703265,0.009074301,0.0000926662],"about_ca_topic_score_codex":0.0000018522287,"about_ca_topic_score_gemma":0.000002038801,"teacher_disagreement_score":0.77980614,"about_ca_system_score_codex":0.00008777137,"about_ca_system_score_gemma":0.0000878443,"threshold_uncertainty_score":0.9837407},"labels":[],"label_agreement":null}]}