{"meta":{"page":1,"per_page":50,"max_per_page":100,"total":609,"total_is_capped":false,"direct_labels_cover":1,"predictions_cover":609,"direct_label_status":"direct model label, unvalidated","prediction_status":"machine_predicted_unvalidated (Codex and Gemma teacher distillation)","score_status":"score_only:v0-immature-baseline (scores rank; they never assert a category)","snapshot":{"source":"OpenAlex, pinned release, all 482 partitions","release":"2026-06-24","frame_built":"2026-07-12","author_layer_release":"2026-06-26"},"query_hash":"7d3c29b2781f","filters":{"topic":"Advanced Mathematical Identities"}},"results":[{"id":"W1827962746","doi":"10.1090/s0002-9947-00-02616-7","title":"Special values of multiple polylogarithms","year":2000,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":369,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Simon Fraser University","funders":"Natural Sciences and Engineering Research Council of Canada; Simon Fraser University","keywords":"Polylogarithm; Mathematics; Conjecture; Harmonic number; Euler's formula; Number theory; Riemann zeta function; Riemann hypothesis; Enumerative combinatorics; Pure mathematics; Algebra over a field; Arithmetic zeta function; Discrete mathematics; Prime zeta function; Mathematical analysis","authors":[{"name":"Jonathan M. Borwein","is_ca":true},{"name":"David M. Bradley","is_ca":false},{"name":"David Broadhurst","is_ca":false},{"name":"Petr Lisoněk","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02517934247070893,"gpt":0.2996648048613165,"spread":0.2744854623906076,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006173227,0.0004941226,0.0005384268,0.001355564,0.001711926,0.003522498,0.0007183132,0.0008384179,0.005705669],"category_scores_gemma":[0.004775467,0.0002801076,0.0003859111,0.0007433249,0.00449158,0.004328116,0.002343355,0.002134804,0.0007409846],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00089468,"about_ca_system_score_gemma":0.0003841635,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002087188,"about_ca_topic_score_gemma":0.0002287264,"domain_scores_codex":[0.9995494,0.00009127962,0.00002222726,0.00008734435,0.0001507357,0.00009884639],"domain_scores_gemma":[0.9988195,0.0005515536,0.000128218,0.000152857,0.0001677267,0.00018001],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002478266,0.000009798402,0.0004650995,0.00003025151,0.000003428768,0.0002080464,0.0001641842,0.000423088,0.0006555105,0.9933633,0.001191219,0.003461296],"study_design_scores_gemma":[0.000007055696,0.00001170099,0.0003170921,0.00002567183,0.000005411637,0.0003636914,0.0001200018,0.002204487,0.0006977845,0.9908071,0.005429542,0.0000104276],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.63426,0.002611239,0.06651387,0.003486858,0.001531042,0.00003677493,0.0001426346,0.0003332596,0.2910844],"genre_scores_gemma":[0.9878462,0.0005306287,0.003709448,0.0001704433,0.0005511036,0.00001497099,0.0000347316,0.0000430932,0.00709945],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005705669,"threshold_uncertainty_score":0.01908731,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2018273723","doi":"10.1016/j.jmaa.2005.01.020","title":"Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials","year":2005,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":254,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Bernoulli polynomials; Pure mathematics; Classical orthogonal polynomials; Discrete orthogonal polynomials; Difference polynomials; Orthogonal polynomials; Generating function; Order (exchange); Wilson polynomials; Combinatorics","authors":[{"name":"Qiu-Ming Luo","is_ca":false},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.0255197784614225,"gpt":0.3119740986445549,"spread":0.2864543201831324,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00208463,0.0007878983,0.00096502,0.002824671,0.001835278,0.002432293,0.001269253,0.001442123,0.005961507],"category_scores_gemma":[0.007678901,0.0004723812,0.001123789,0.002802253,0.003806179,0.005529569,0.001792619,0.003336717,0.0007381887],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001532438,"about_ca_system_score_gemma":0.001081667,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001338248,"about_ca_topic_score_gemma":0.001177103,"domain_scores_codex":[0.9993563,0.0002041698,0.00004309563,0.0001320648,0.0001745628,0.00008980924],"domain_scores_gemma":[0.9978176,0.0008922802,0.0003767053,0.0002184086,0.0003492184,0.0003457069],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000007266714,0.000006220021,0.0001069734,0.0000181693,0.000002558848,0.00004788025,0.00006696323,0.000464267,0.0001174914,0.9958491,0.0006189966,0.002694177],"study_design_scores_gemma":[0.000005795759,0.000007363363,0.0001590082,0.00001075158,0.000003404974,0.0001094809,0.00002808924,0.003186102,0.00005696153,0.9930452,0.003379117,0.00000872342],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3241327,0.01934994,0.3513859,0.01247505,0.004424591,0.00009148994,0.0006075889,0.0002578426,0.287275],"genre_scores_gemma":[0.884626,0.01129918,0.0438824,0.001447006,0.007773328,0.00009594357,0.0003345501,0.0001176561,0.05042391],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005961507,"threshold_uncertainty_score":0.01994324,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1998239757","doi":"10.4153/cjm-2004-002-2","title":"Ternary Diophantine Equations via Galois Representations and Modular Forms","year":2004,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":206,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Diophantine equation; Galois module; Ternary operation; Galois group; Polynomial; Algebra over a field; Exponential function; Pure mathematics; Discrete mathematics; Mathematical analysis","authors":[{"name":"Michael A. Bennett","is_ca":true},{"name":"Chris M. Skinner","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03858730027078191,"gpt":0.3028448578213384,"spread":0.2642575575505565,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009021913,0.0004077169,0.0005674395,0.0008108756,0.0007138699,0.001269449,0.0009237495,0.0006757601,0.004729305],"category_scores_gemma":[0.003609558,0.0002160367,0.0006772333,0.0007175017,0.00150968,0.001993681,0.001521267,0.001886381,0.0005892374],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008214176,"about_ca_system_score_gemma":0.0007691716,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009327946,"about_ca_topic_score_gemma":0.001423742,"domain_scores_codex":[0.9993723,0.0001228646,0.00004476733,0.0000710873,0.000301333,0.00008767385],"domain_scores_gemma":[0.9995052,0.0002169537,0.00006910314,0.00007904368,0.00008365126,0.00004613739],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001523465,0.00002089755,0.000256075,0.00005217543,0.000009102748,0.0001095422,0.0001397729,0.007454457,0.002057881,0.9785258,0.001081961,0.01027711],"study_design_scores_gemma":[0.00005569307,0.00003026077,0.0003251197,0.0000321045,0.00001596297,0.0003234658,0.0001301176,0.1300842,0.00570863,0.8556909,0.007575081,0.00002836286],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2694662,0.0009040451,0.6619497,0.001809233,0.000525287,0.000164192,0.0002520827,0.0002524471,0.06467675],"genre_scores_gemma":[0.8420154,0.0006902135,0.1392474,0.000372232,0.0002559191,0.00007890834,0.0001352724,0.00007364302,0.01713094],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004729305,"threshold_uncertainty_score":0.0158211,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2129840940","doi":"10.1017/s0305004100004412","title":"Some formulas for the Bernoulli and Euler polynomials at rational arguments","year":2000,"lang":"en","type":"article","venue":"Mathematical Proceedings of the Cambridge Philosophical Society","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":202,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Euler's formula; Bernoulli's principle; Bernoulli polynomials; Mathematics; Pure mathematics; Algebra over a field; Applied mathematics; Mathematical analysis; Orthogonal polynomials; Difference polynomials; Physics; Thermodynamics","authors":[{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04154337426295546,"gpt":0.2936462034272952,"spread":0.2521028291643398,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002056234,0.001200987,0.0006032403,0.00322244,0.001605256,0.002511736,0.002221741,0.001570344,0.01083922],"category_scores_gemma":[0.007696433,0.0006479473,0.0009085239,0.002802831,0.002412671,0.00705255,0.001615564,0.004558956,0.002651741],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001775524,"about_ca_system_score_gemma":0.0007878904,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001373483,"about_ca_topic_score_gemma":0.001856941,"domain_scores_codex":[0.9993551,0.0001487095,0.00005942518,0.00007959821,0.0002709129,0.00008615775],"domain_scores_gemma":[0.9989488,0.0004754531,0.0001194918,0.00009719591,0.0002906947,0.00006851643],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005496438,0.000007726731,0.00004694357,0.00004431813,0.000002379727,0.00006416107,0.0001114006,0.0002544361,0.0003767124,0.9880424,0.002309659,0.008734315],"study_design_scores_gemma":[0.000006017831,0.000009627624,0.0001723774,0.00004103634,0.00000687682,0.0001800786,0.00004433651,0.003992405,0.0005292735,0.9790293,0.01596953,0.00001920941],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.04401815,0.01707996,0.6920441,0.01194624,0.00385953,0.0001591611,0.0008941902,0.0004767723,0.2295219],"genre_scores_gemma":[0.4286421,0.02274093,0.4238714,0.004885573,0.006795294,0.0005372467,0.0009061678,0.000643703,0.1109776],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.01083922,"threshold_uncertainty_score":0.03626084,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2066932187","doi":"10.1016/s0893-9659(04)90077-8","title":"Remarks on some relationships between the Bernoulli and Euler polynomials","year":2004,"lang":"en","type":"article","venue":"Applied Mathematics Letters","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":185,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Bernoulli's principle; Euler's formula; Object (grammar); Bernoulli polynomials; Euler number (physics); Pure mathematics; Algebra over a field; Difference polynomials; Orthogonal polynomials; Euler equations; Mathematical analysis; Semi-implicit Euler method; Backward Euler method; Artificial intelligence; Computer science","authors":[{"name":"H. M. Srivastava","is_ca":true},{"name":"Ákos Pintér","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.05245962952805756,"gpt":0.2856882822586929,"spread":0.2332286527306353,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00443229,0.001021793,0.0009254258,0.002110444,0.003125461,0.003091223,0.002205652,0.002722128,0.02350694],"category_scores_gemma":[0.01297316,0.0005122322,0.000892607,0.001716601,0.006463239,0.00946619,0.002564007,0.00534013,0.002927035],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001160646,"about_ca_system_score_gemma":0.0004419168,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001388377,"about_ca_topic_score_gemma":0.001126482,"domain_scores_codex":[0.9985716,0.0005759615,0.00007538245,0.0002495708,0.0004153178,0.0001121442],"domain_scores_gemma":[0.9925358,0.005014874,0.0006299027,0.0005783568,0.0008754161,0.0003656319],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003952816,0.00001459514,0.0001676893,0.00007862327,0.000008945107,0.0002120572,0.0003275264,0.0002636391,0.0002493517,0.9834859,0.01194125,0.003210826],"study_design_scores_gemma":[0.00001401652,0.0000135843,0.0003826268,0.00004196613,0.000007074507,0.000140104,0.0001341114,0.0004852262,0.0002018678,0.9717228,0.02684309,0.00001365521],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.04130065,0.01500808,0.1639497,0.2251497,0.0180976,0.0001181719,0.001117554,0.0006840549,0.5345745],"genre_scores_gemma":[0.6882403,0.01400149,0.07541011,0.0634036,0.03144798,0.0003620645,0.0007805304,0.000588612,0.1257653],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02350694,"threshold_uncertainty_score":0.07863855,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2034149193","doi":"10.1016/j.amc.2010.12.048","title":"Some generalizations of the Apostol–Genocchi polynomials and the Stirling numbers of the second kind","year":2010,"lang":"en","type":"article","venue":"Applied Mathematics and Computation","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":167,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Orthogonal polynomials; Difference polynomials; Discrete orthogonal polynomials; Classical orthogonal polynomials; Wilson polynomials; Pure mathematics; Stirling number; Bernoulli polynomials; Hahn polynomials; Macdonald polynomials; Generating function; Gegenbauer polynomials; Discrete mathematics","authors":[{"name":"Qiu-Ming Luo","is_ca":false},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.01877722999568428,"gpt":0.2741288941244537,"spread":0.2553516641287695,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001345804,0.0008351297,0.0007304191,0.003089107,0.001323945,0.002439811,0.0009920213,0.001255895,0.004964063],"category_scores_gemma":[0.004757556,0.0003683882,0.001216032,0.002370223,0.003102985,0.00332407,0.001258159,0.002770224,0.0009582863],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001687028,"about_ca_system_score_gemma":0.0009796222,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001374778,"about_ca_topic_score_gemma":0.001305926,"domain_scores_codex":[0.9995993,0.0001155618,0.00002487729,0.00007780848,0.0001090017,0.0000734354],"domain_scores_gemma":[0.9989681,0.0003936534,0.0001863264,0.0001308311,0.0001704897,0.0001504763],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001638493,0.000006436008,0.00008874042,0.00003877218,0.000003818995,0.00008054318,0.00008980452,0.0007029193,0.0003596692,0.9930565,0.0009367462,0.004619784],"study_design_scores_gemma":[0.000010545,0.00001504116,0.0003113462,0.00002096355,0.000006346158,0.0002583035,0.00004918129,0.004643122,0.0002574805,0.986855,0.007553851,0.00001872831],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3314306,0.03227884,0.230822,0.008784421,0.004759402,0.00009533465,0.0005450629,0.0003541303,0.3909301],"genre_scores_gemma":[0.891269,0.01135842,0.03672983,0.001190071,0.005496727,0.00008193927,0.000290679,0.0001393577,0.05344399],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004964063,"threshold_uncertainty_score":0.01660639,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2044270276","doi":"10.1016/j.camwa.2005.04.018","title":"Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials","year":2006,"lang":"en","type":"article","venue":"Computers & Mathematics with Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":161,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Pure mathematics; Orthogonal polynomials; Bernoulli polynomials; Euler's formula; Order (exchange); Bernoulli's principle; Stirling numbers of the second kind; Object (grammar); Classical orthogonal polynomials; Difference polynomials; Mathematical analysis; Computer science; Artificial intelligence","authors":[{"name":"Qiu-Ming Luo","is_ca":false},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04202564462604295,"gpt":0.2859267698731662,"spread":0.2439011252471232,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002306201,0.0006930141,0.0007411717,0.003071641,0.002157071,0.00293048,0.001129595,0.001450315,0.007105923],"category_scores_gemma":[0.01177167,0.0005384465,0.0005815962,0.003295199,0.004237867,0.005508686,0.001969532,0.004243982,0.0008602242],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001566136,"about_ca_system_score_gemma":0.0007936508,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001034813,"about_ca_topic_score_gemma":0.0009677178,"domain_scores_codex":[0.9993254,0.0002643526,0.00003664571,0.0001374915,0.0001579644,0.00007811045],"domain_scores_gemma":[0.9956358,0.002675863,0.0006234757,0.0002014043,0.0004662825,0.0003971081],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000009284885,0.00000766406,0.0001357885,0.00001268961,0.000001958205,0.00003162367,0.00007115747,0.0002921502,0.00007922504,0.9967971,0.000447039,0.002114416],"study_design_scores_gemma":[0.000005875536,0.000007775809,0.000169005,0.00001127283,0.000003363249,0.00005974923,0.00003217974,0.002729216,0.00006028093,0.995073,0.001839761,0.000008329259],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4204335,0.01724658,0.26288,0.01328707,0.002222559,0.00009055858,0.0005033214,0.0001819918,0.2831544],"genre_scores_gemma":[0.9307029,0.00625711,0.03121745,0.001248513,0.002762697,0.00008501651,0.0002363375,0.00008682859,0.02740301],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007105923,"threshold_uncertainty_score":0.02377164,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2086306912","doi":"10.1016/j.camwa.2010.09.031","title":"A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials","year":2010,"lang":"en","type":"article","venue":"Computers & Mathematics with Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":138,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Difference polynomials; Bernoulli polynomials; Classical orthogonal polynomials; Discrete orthogonal polynomials; Generating function; Wilson polynomials; Euler's formula; Pure mathematics; Hahn polynomials; Orthogonal polynomials; Gegenbauer polynomials; Unification; Algebra over a field; Applied mathematics; Mathematical analysis","authors":[{"name":"Hacer Özden","is_ca":false},{"name":"Yılmaz Şimşek","is_ca":false},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02446023330750461,"gpt":0.2833333808487741,"spread":0.2588731475412695,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001419249,0.001254094,0.001192107,0.003849124,0.001446162,0.003434433,0.001494399,0.001577538,0.008368328],"category_scores_gemma":[0.002126444,0.0003789569,0.0009119688,0.002643162,0.002519088,0.003206917,0.001404396,0.002585195,0.001768858],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001263754,"about_ca_system_score_gemma":0.001021629,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001049567,"about_ca_topic_score_gemma":0.0009500336,"domain_scores_codex":[0.999473,0.000188312,0.00002930052,0.00006850912,0.0001642565,0.00007649986],"domain_scores_gemma":[0.9995129,0.0001504124,0.00006101839,0.00007763395,0.0001345894,0.00006337761],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000002674665,0.000002029861,0.00001800429,0.0000131379,0.000001037322,0.00002658713,0.00005056319,0.0003323146,0.0001782077,0.9963652,0.0007374614,0.00227267],"study_design_scores_gemma":[0.000003445198,0.000008116599,0.00006405544,0.0000197945,0.000003303831,0.0001563195,0.00003705237,0.004418663,0.0001538458,0.9835058,0.01161937,0.00001033425],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07250874,0.01757339,0.5849059,0.006298337,0.003975377,0.0001342279,0.0006619102,0.0005641539,0.3133779],"genre_scores_gemma":[0.6905038,0.01411737,0.2026817,0.002346689,0.006325906,0.0003730699,0.0006663597,0.0005548472,0.08243032],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008368328,"threshold_uncertainty_score":0.02799487,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1972887519","doi":"10.2977/prims/47","title":"The Laplace Transform of the Cut-and-Join Equation and the Bouchard–Mariño Conjecture on Hurwitz Numbers","year":2011,"lang":"en","type":"article","venue":"Publications of the Research Institute for Mathematical Sciences","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":109,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"","funders":"European Science Foundation; Fonds Québécois de la Recherche sur la Nature et les Technologies; Agence Nationale de la Recherche; American Institute of Mathematics; National Science Foundation","keywords":"Conjecture; Laplace transform; Mathematics; Join (topology); Pure mathematics; Mathematical analysis; Combinatorics","authors":[{"name":"Bertrand Eynard","is_ca":false},{"name":"Motohico Mulase","is_ca":false},{"name":"Bradley Safnuk","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.2893276168169053,"gpt":0.4231946774122988,"spread":0.1338670605953935,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00081449,0.0003796016,0.0005040644,0.001771203,0.0006747546,0.00152123,0.0008833059,0.0009673219,0.00522209],"category_scores_gemma":[0.004270069,0.0002078233,0.0005957565,0.0007915878,0.00189667,0.003124641,0.001435091,0.001673833,0.0007093739],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008752487,"about_ca_system_score_gemma":0.0006402929,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001382708,"about_ca_topic_score_gemma":0.0009665692,"domain_scores_codex":[0.9997302,0.0000573974,0.0000100271,0.0000312269,0.0001229143,0.00004827873],"domain_scores_gemma":[0.9993603,0.0002667439,0.0001007725,0.00005401441,0.0001203029,0.00009784879],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002204415,0.0000222589,0.0006460253,0.00002455687,0.000004877663,0.0001596277,0.0001741513,0.002691696,0.002047904,0.9876885,0.0007674381,0.005750845],"study_design_scores_gemma":[0.0000298237,0.00002715104,0.0009314337,0.00002287149,0.000009576283,0.0002160171,0.0001449729,0.09241782,0.002260756,0.9022804,0.00163067,0.00002846395],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7761857,0.001104986,0.1505852,0.002848466,0.0003227468,0.0000651757,0.0001028159,0.0003381977,0.06844682],"genre_scores_gemma":[0.9765713,0.000379814,0.0110918,0.0002064668,0.0002388438,0.00003711039,0.00008171066,0.0000831439,0.01130974],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00522209,"threshold_uncertainty_score":0.01746958,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2111280161","doi":"10.1080/10652469.2010.530128","title":"Integral and computational representations of the extended Hurwitz–Lerch zeta function","year":2011,"lang":"en","type":"article","venue":"Integral Transforms and Special Functions","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":100,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Pure mathematics; Continuation; Polylogarithm; Bernoulli polynomials; Analytic continuation; Riemann zeta function; Hypergeometric function; Algebra over a field; Arithmetic zeta function; Mathematical analysis; Prime zeta function","authors":[{"name":"H. M. Srivastava","is_ca":true},{"name":"Ram K. Saxena","is_ca":false},{"name":"Tibor K. Pogány","is_ca":false},{"name":"Ravi Saxena","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.06708238984146644,"gpt":0.304065859778706,"spread":0.2369834699372395,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001686001,0.0005891931,0.0007293035,0.001662088,0.0009709732,0.003666901,0.001357604,0.000718117,0.004652537],"category_scores_gemma":[0.005926185,0.0002519089,0.001145271,0.001361298,0.002310353,0.006761903,0.001923652,0.002051409,0.0006912371],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00132739,"about_ca_system_score_gemma":0.0009226191,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005934329,"about_ca_topic_score_gemma":0.0004098766,"domain_scores_codex":[0.9991063,0.0002343398,0.00005357442,0.0001084085,0.0003493318,0.0001479859],"domain_scores_gemma":[0.9984828,0.0006907167,0.0001117789,0.0003740821,0.0002380175,0.000102645],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0000114753,0.00001627089,0.0002190702,0.0000311802,0.000003858234,0.00005246439,0.000174192,0.00373231,0.000539262,0.9862496,0.000400976,0.008569403],"study_design_scores_gemma":[0.000009133982,0.00001844369,0.000214345,0.00003814896,0.000009986634,0.0001665177,0.0001142845,0.0894436,0.001219456,0.90325,0.005496367,0.00001976616],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2029519,0.002324594,0.7276798,0.001619322,0.0002331015,0.00009825743,0.0001554116,0.0003160378,0.06462148],"genre_scores_gemma":[0.8450974,0.002078597,0.1403687,0.0002351391,0.0004670752,0.0001368558,0.0002137838,0.0001675546,0.01123497],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004652537,"threshold_uncertainty_score":0.01556426,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2321170195","doi":"10.1134/s1061920810020093","title":"A new generalization of the Bernoulli and related polynomials","year":2010,"lang":"en","type":"article","venue":"Russian Journal of Mathematical Physics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":87,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Generalization; Mathematics; Bernoulli polynomials; Bernoulli's principle; Pure mathematics; Combinatorics; Algebra over a field; Orthogonal polynomials; Discrete orthogonal polynomials; Mathematical analysis; Physics","authors":[{"name":"H. M. Srivastava","is_ca":true},{"name":"Mridula Garg","is_ca":false},{"name":"Sangeeta Choudhary","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.01870872941432779,"gpt":0.2878998769034372,"spread":0.2691911474891094,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000559171,0.0003869486,0.0005272399,0.001200348,0.0007968302,0.0009349568,0.0007412696,0.0008291572,0.00256619],"category_scores_gemma":[0.001560059,0.0001935846,0.0005453221,0.001043131,0.001493068,0.00254217,0.0009352362,0.001301697,0.0004239342],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005407824,"about_ca_system_score_gemma":0.0008457465,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006520492,"about_ca_topic_score_gemma":0.0005694073,"domain_scores_codex":[0.9996672,0.00006916089,0.00001173662,0.0000747352,0.0001093236,0.00006794296],"domain_scores_gemma":[0.9996023,0.0001009789,0.00007129023,0.00005087378,0.00008658684,0.0000880647],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000008060831,0.00001071931,0.0001727388,0.00002610733,0.000002594125,0.0001282364,0.00008375342,0.00226108,0.002048301,0.9889783,0.0005807081,0.005699418],"study_design_scores_gemma":[0.00001521946,0.00006134139,0.0005571682,0.00002715264,0.000008887776,0.001015503,0.00008389741,0.05802565,0.001334669,0.9224476,0.01638255,0.00004039066],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4185703,0.003687226,0.4818511,0.002940142,0.001832761,0.0001241364,0.0002797697,0.0003940553,0.09032053],"genre_scores_gemma":[0.9064375,0.002244712,0.06183789,0.0007800446,0.001839558,0.00008257693,0.0001620807,0.0001173484,0.02649819],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00256619,"threshold_uncertainty_score":0.008584738,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1981006054","doi":"10.1016/j.mcm.2011.05.032","title":"Some summation formulas involving harmonic numbers and generalized harmonic numbers","year":2011,"lang":"en","type":"article","venue":"Mathematical and Computer Modelling","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":87,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"Natural Sciences and Engineering Research Council of Canada; Ministry of Education, Science and Technology","keywords":"Harmonic number; Harmonic; Mathematics; Series (stratigraphy); Range (aeronautics); Harmonic analysis; Number theory; Mathematical analysis; Pure mathematics; Physics; Quantum mechanics","authors":[{"name":"Junesang Choi","is_ca":false},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.1087266322358916,"gpt":0.2773350123929414,"spread":0.1686083801570498,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001838512,0.001079534,0.001027084,0.002218775,0.001904151,0.002949512,0.00168294,0.001254618,0.007314664],"category_scores_gemma":[0.004996222,0.0004817303,0.001025692,0.002995816,0.002395976,0.007559033,0.002159906,0.003024638,0.001499059],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00110616,"about_ca_system_score_gemma":0.0006835981,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004919776,"about_ca_topic_score_gemma":0.0007126823,"domain_scores_codex":[0.9992124,0.0002188553,0.00007066526,0.0001068374,0.0003096934,0.00008150698],"domain_scores_gemma":[0.9988809,0.0004837675,0.0001119974,0.0001451002,0.0002681017,0.0001099968],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005506903,0.000006783885,0.00005073475,0.00003634022,0.000004903718,0.00007080076,0.0001214536,0.0002184822,0.0004414731,0.9915864,0.001376816,0.006080337],"study_design_scores_gemma":[0.000002485073,0.000005260237,0.00007550231,0.00001260269,0.000008868793,0.0001668951,0.00003159271,0.004006216,0.0003028188,0.9906797,0.00469821,0.000009901689],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1155377,0.01165737,0.6251946,0.003626591,0.003809195,0.00008283776,0.0003322768,0.0003398049,0.2394196],"genre_scores_gemma":[0.6723429,0.008771078,0.1898009,0.001798596,0.005056146,0.0001909566,0.0004232782,0.0006492566,0.1209668],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007314664,"threshold_uncertainty_score":0.02446997,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2073328732","doi":"10.1016/j.jnt.2006.08.009","title":"Convolution identities and lacunary recurrences for Bernoulli numbers","year":2006,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":83,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Dalhousie University","funders":"","keywords":"Mathematics; Bernoulli number; Bernoulli polynomials; Stirling numbers of the first kind; Stirling numbers of the second kind; Lacunary function; Recurrence relation; Bernoulli's principle; Convolution (computer science); Quadratic equation; Euler's formula; Discrete mathematics; Combinatorics; Stirling number; Pure mathematics; Mathematical analysis; Difference polynomials","authors":[{"name":"Takashi Agoh","is_ca":false},{"name":"Karl Dilcher","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02998956073953729,"gpt":0.3411240122598801,"spread":0.3111344515203428,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003256092,0.001088025,0.001346058,0.00292765,0.003359534,0.005561627,0.001598586,0.001824589,0.005274004],"category_scores_gemma":[0.01027257,0.0007416366,0.001241462,0.002829653,0.005124813,0.008384956,0.003059125,0.004762535,0.001234522],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002833198,"about_ca_system_score_gemma":0.001338772,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001906356,"about_ca_topic_score_gemma":0.001867078,"domain_scores_codex":[0.998607,0.000325458,0.0001202667,0.0002115115,0.0004917202,0.0002440399],"domain_scores_gemma":[0.996982,0.001408226,0.0004368064,0.0003384452,0.0005098672,0.0003246001],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000007627076,0.000004210103,0.00006112467,0.00000989339,0.000001887943,0.00003828208,0.0001399082,0.0001480968,0.0001904142,0.9974207,0.0003665952,0.001611387],"study_design_scores_gemma":[0.000003549672,0.000003592172,0.00005978995,0.000005229232,0.00000321072,0.00006610511,0.00002154258,0.001517316,0.0001217437,0.9969313,0.001258803,0.000007759314],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3115599,0.009564614,0.4395399,0.006132247,0.002721876,0.00009623136,0.000321899,0.0004623557,0.2296011],"genre_scores_gemma":[0.897082,0.002760513,0.04893017,0.00106953,0.00187886,0.0001204071,0.0002069868,0.0001959104,0.04775553],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005561627,"threshold_uncertainty_score":0.02055639,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2015423229","doi":"10.1016/j.jnt.2013.03.004","title":"A unified presentation of three families of generalized Apostol type polynomials based upon the theory of the umbral calculus and the umbral algebra","year":2013,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":80,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Wilson polynomials; Difference polynomials; Macdonald polynomials; Classical orthogonal polynomials; Discrete orthogonal polynomials; Hahn polynomials; Orthogonal polynomials; Koornwinder polynomials; Algebra over a field; Pure mathematics; Gegenbauer polynomials","authors":[{"name":"Rahime Dere","is_ca":false},{"name":"Yılmaz Şimşek","is_ca":false},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03225895475894939,"gpt":0.2983150721526861,"spread":0.2660561173937367,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00118969,0.0008076229,0.0009758296,0.002751554,0.002862654,0.004473155,0.001498355,0.001437484,0.007932862],"category_scores_gemma":[0.001981418,0.000280889,0.001038632,0.001629597,0.003970578,0.004635633,0.002006203,0.002145851,0.001127108],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001729453,"about_ca_system_score_gemma":0.00105183,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000719759,"about_ca_topic_score_gemma":0.000659159,"domain_scores_codex":[0.9993681,0.0001741415,0.00003276606,0.00008197872,0.0002189022,0.000124138],"domain_scores_gemma":[0.9993548,0.0001289269,0.0001070888,0.0000987497,0.0001466017,0.0001638444],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005066872,0.000002466664,0.00002181841,0.00001096697,0.000001041321,0.00004656366,0.00008513415,0.0001275648,0.0001791944,0.9977713,0.0002806488,0.001468313],"study_design_scores_gemma":[0.000005352089,0.00001143312,0.00006326848,0.00001913877,0.00000382089,0.0001922518,0.0001055896,0.003062526,0.0002342208,0.9885438,0.007746691,0.00001198743],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1379268,0.006239505,0.5496765,0.005214951,0.002294968,0.0001602591,0.0003602585,0.0006365949,0.2974902],"genre_scores_gemma":[0.8555235,0.003154828,0.09548158,0.001025583,0.001433328,0.0001857842,0.0002282015,0.0001874838,0.04277975],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007932862,"threshold_uncertainty_score":0.02653807,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1986176257","doi":"10.4153/cmb-2007-028-9","title":"Second Order Mock Theta Functions","year":2007,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":78,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"about_ca":false},"ca_institutions":"University of Regina","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Ramanujan theta function; Ramanujan's sum; Order (exchange); Theta function; Combinatorics; Pure mathematics","authors":[{"name":"Richard J. McIntosh","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02837560933620055,"gpt":0.2823304327914562,"spread":0.2539548234552557,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001067325,0.0005422038,0.0004781236,0.001512827,0.001306805,0.00206887,0.0005631311,0.0008829609,0.006126784],"category_scores_gemma":[0.004863848,0.0002833747,0.0007027535,0.0006271065,0.002515125,0.002811222,0.001444292,0.001784673,0.001251838],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00132618,"about_ca_system_score_gemma":0.0006565414,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008592019,"about_ca_topic_score_gemma":0.0004438431,"domain_scores_codex":[0.9994056,0.0001434758,0.00002161329,0.00008084868,0.0002104717,0.0001379357],"domain_scores_gemma":[0.9984782,0.0003214121,0.0001741192,0.0002311417,0.0004531845,0.0003419124],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001455976,0.000004635675,0.0003342794,0.00001133014,0.000002785064,0.00005213881,0.0001294027,0.0006406704,0.0007446308,0.9940251,0.0006567118,0.003383853],"study_design_scores_gemma":[0.000008508221,0.00003642264,0.0008817981,0.00002481599,0.000005519519,0.0004725289,0.0001381899,0.008962077,0.001265221,0.9721428,0.01603713,0.00002518625],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5493814,0.002468563,0.2072417,0.003490158,0.001096343,0.00006705149,0.0002561728,0.0004871711,0.2355115],"genre_scores_gemma":[0.9414246,0.0006158508,0.01386024,0.0003185864,0.000394865,0.00005443291,0.0001062991,0.00008904009,0.04313619],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006126784,"threshold_uncertainty_score":0.02049613,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2045698952","doi":"10.1016/j.amc.2007.10.033","title":"Some q-extensions of the Apostol–Bernoulli and the Apostol–Euler polynomials of order n, and the multiple Hurwitz zeta function","year":2007,"lang":"en","type":"article","venue":"Applied Mathematics and Computation","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":77,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Bernoulli polynomials; Hurwitz polynomial; Order (exchange); Generalization; Pure mathematics; Polylogarithm; Euler's formula; Bernoulli's principle; Generating function; Function (biology); Riemann zeta function; Combinatorics; Classical orthogonal polynomials; Orthogonal polynomials; Arithmetic zeta function; Mathematical analysis; Prime zeta function; Polynomial; Physics","authors":[{"name":"Junesang Choi","is_ca":false},{"name":"P.J. Anderson","is_ca":true},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02288902419903421,"gpt":0.273682356617451,"spread":0.2507933324184168,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001213454,0.0009248899,0.0006629444,0.002591445,0.002316417,0.002411161,0.0009454262,0.001001294,0.003656429],"category_scores_gemma":[0.003971138,0.0004113778,0.0007515752,0.001526081,0.004053281,0.003530021,0.001950601,0.002125313,0.0005097327],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00164687,"about_ca_system_score_gemma":0.0009668334,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001397859,"about_ca_topic_score_gemma":0.001117471,"domain_scores_codex":[0.9996077,0.0001184287,0.00002107862,0.00006857071,0.0001064077,0.00007772036],"domain_scores_gemma":[0.9985607,0.0004245872,0.0003333008,0.0000731295,0.0001551174,0.0004531961],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00004469692,0.00001831556,0.0002922719,0.00002423954,0.000005629236,0.0002181663,0.0001844776,0.000796922,0.0005664632,0.9949868,0.0005115574,0.002350679],"study_design_scores_gemma":[0.00001992688,0.0000235683,0.0005518754,0.00001805205,0.000005545719,0.00025647,0.0000934064,0.004168145,0.0002394405,0.9924701,0.00213696,0.00001645366],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8219295,0.00377541,0.05457893,0.003667248,0.0008902065,0.00004118645,0.0001852986,0.0001247289,0.1148075],"genre_scores_gemma":[0.9699264,0.001234316,0.005707846,0.0003101408,0.0009536608,0.00003614815,0.0001152975,0.00003482416,0.02168139],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003656429,"threshold_uncertainty_score":0.01223195,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2049550791","doi":"10.1016/j.jnt.2006.09.017","title":"Transcendental values of the digamma function","year":2007,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":75,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Queen's University","funders":"","keywords":"Digamma function; Mathematics; Transcendental number; Transcendental function; Algebraic number; Euler's formula; Logarithm; Constant (computer programming); Integer (computer science); Pure mathematics; Combinatorics; Discrete mathematics; Riemann zeta function; Mathematical analysis","authors":[{"name":"M. Ram Murty","is_ca":true},{"name":"N. Saradha","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02637769298064774,"gpt":0.3261222277948047,"spread":0.2997445348141569,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001252835,0.001079404,0.0008766706,0.004932031,0.002292345,0.004768999,0.001489553,0.00138182,0.008127015],"category_scores_gemma":[0.004980625,0.0004853859,0.0007222687,0.001858375,0.004726882,0.005674612,0.002293095,0.003683542,0.002088327],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00202657,"about_ca_system_score_gemma":0.0007594755,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005215938,"about_ca_topic_score_gemma":0.0004962027,"domain_scores_codex":[0.9993777,0.0001735711,0.00003417297,0.0001258874,0.0001682274,0.0001204689],"domain_scores_gemma":[0.9979207,0.0009074245,0.0001635047,0.0003162017,0.0003231231,0.0003691012],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001525297,0.000008645153,0.00008916122,0.00001612935,0.000004422153,0.00005500911,0.00008091239,0.0002321636,0.000445351,0.9951807,0.0005389081,0.003333263],"study_design_scores_gemma":[0.000005235217,0.000005061087,0.000112721,0.00001088938,0.000003784367,0.00012749,0.00002390817,0.001410336,0.0003839265,0.9958304,0.002075735,0.00001059305],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.32927,0.005522382,0.1656846,0.00582289,0.001501491,0.00003718349,0.0003835311,0.0005596111,0.4912184],"genre_scores_gemma":[0.9497516,0.001340269,0.01450458,0.0006720878,0.0008217951,0.00004409389,0.000154724,0.0001524678,0.03255846],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008127015,"threshold_uncertainty_score":0.02718753,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2076463309","doi":"10.1007/s11139-007-9083-z","title":"The evaluation of character Euler double sums","year":2008,"lang":"en","type":"article","venue":"The Ramanujan Journal","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":75,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Dalhousie University","funders":"","keywords":"Riemann zeta function; Combinatorics; Mathematics; Character (mathematics); Riemann hypothesis; Euler's formula; Dirichlet distribution; Function (biology); Pure mathematics; Mathematical analysis; Geometry","authors":[{"name":"Jonathan M. Borwein","is_ca":true},{"name":"I. J. Zucker","is_ca":false},{"name":"J. Boersma","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.2363299532253338,"gpt":0.3961747134056885,"spread":0.1598447601803547,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002158774,0.001270186,0.00113291,0.004515825,0.002307096,0.004976566,0.001325353,0.001031202,0.007343608],"category_scores_gemma":[0.007293647,0.0005826848,0.0006399967,0.001776113,0.004562407,0.00698732,0.003105688,0.002382254,0.001103241],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00214753,"about_ca_system_score_gemma":0.00093839,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007515097,"about_ca_topic_score_gemma":0.0007778921,"domain_scores_codex":[0.9988751,0.0003328342,0.00005535694,0.0001430489,0.0003892391,0.0002043486],"domain_scores_gemma":[0.9982487,0.0006307133,0.0001658241,0.0001927048,0.0003800492,0.0003820617],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00005980096,0.0000215138,0.000299891,0.00004928734,0.000008315113,0.0001060241,0.0002859184,0.000898772,0.0009581582,0.9885396,0.0007406961,0.00803188],"study_design_scores_gemma":[0.00001111743,0.00001558991,0.0003075168,0.00003381361,0.00001136651,0.0001645515,0.0001033801,0.007378948,0.001590446,0.9873861,0.002975609,0.00002162967],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6574866,0.0026915,0.1090023,0.002359693,0.001219975,0.00006567601,0.0001702449,0.000437705,0.2265663],"genre_scores_gemma":[0.9521236,0.0008986709,0.01133621,0.0001885818,0.0005159092,0.00003749976,0.00012895,0.0002290298,0.03454164],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007343608,"threshold_uncertainty_score":0.02456683,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2041349517","doi":"10.1007/s11139-010-9228-3","title":"Identities for the harmonic numbers and binomial coefficients","year":2010,"lang":"en","type":"article","venue":"The Ramanujan Journal","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":73,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Binomial coefficient; Harmonic number; Mathematics; Number theory; Central binomial coefficient; Binomial approximation; Euler's formula; Binomial (polynomial); Gaussian binomial coefficient; Harmonic; Binomial theorem; Euler number (physics); Binomial distribution; Pure mathematics; Negative binomial distribution; Mathematical analysis; Discrete mathematics; Statistics; Riemann zeta function; Backward Euler method; Euler equations","authors":[{"name":"Anthony Sofo","is_ca":false},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04341133961366769,"gpt":0.3372646372638133,"spread":0.2938532976501457,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002321756,0.001058185,0.001006688,0.004488719,0.002573536,0.00500139,0.001463238,0.001894376,0.01035244],"category_scores_gemma":[0.00666692,0.0006638799,0.0009448004,0.002319017,0.004558114,0.006427485,0.002854259,0.004635774,0.002590473],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002003615,"about_ca_system_score_gemma":0.001243181,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001731109,"about_ca_topic_score_gemma":0.001492628,"domain_scores_codex":[0.9988519,0.0003386534,0.00006245869,0.0001513114,0.0004575317,0.0001381358],"domain_scores_gemma":[0.9983546,0.0007084819,0.0001717729,0.000184209,0.0003569215,0.0002239895],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00000251284,0.000003986641,0.0000264501,0.00001238824,0.0000012382,0.00001484244,0.00007680228,0.000104789,0.000141096,0.9971139,0.0006672033,0.001834729],"study_design_scores_gemma":[0.000003732963,0.000002746745,0.00007668469,0.00001108384,0.000001741582,0.00004059854,0.00002506514,0.0009248948,0.00006981921,0.9958504,0.002985546,0.000007692234],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.1406877,0.01803836,0.2431163,0.008598888,0.005375782,0.0000969489,0.0006340024,0.0002634754,0.5831885],"genre_scores_gemma":[0.7882283,0.01359681,0.06644241,0.001994537,0.006953747,0.0002482311,0.0005263162,0.0002823704,0.1217274],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01035244,"threshold_uncertainty_score":0.03463233,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2127202408","doi":"10.1080/10652469.2011.643627","title":"Some families of Genocchi type polynomials and their interpolation functions","year":2012,"lang":"en","type":"article","venue":"Integral Transforms and Special Functions","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":71,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Difference polynomials; Orthogonal polynomials; Interpolation (computer graphics); Type (biology); Classical orthogonal polynomials; Discrete orthogonal polynomials; Algebra over a field; Pure mathematics; Wilson polynomials; Gegenbauer polynomials; Macdonald polynomials; Artificial intelligence; Computer science","authors":[{"name":"H. M. Srivastava","is_ca":true},{"name":"Burak Kurt","is_ca":false},{"name":"Yılmaz Şimşek","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04126118493710859,"gpt":0.2882539422159174,"spread":0.2469927572788088,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008334209,0.0004626159,0.0003720135,0.001582741,0.001099441,0.0007035677,0.0006835597,0.0005589176,0.003274201],"category_scores_gemma":[0.002023968,0.0001873246,0.0006282213,0.0009430111,0.001231882,0.001071933,0.000677161,0.001200779,0.0003855254],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00107063,"about_ca_system_score_gemma":0.0005969558,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001250793,"about_ca_topic_score_gemma":0.0008790679,"domain_scores_codex":[0.9996514,0.0001072603,0.00001001882,0.00004585973,0.0001020168,0.00008347954],"domain_scores_gemma":[0.9993927,0.0002253777,0.0001107887,0.00005755043,0.0001235262,0.00008997488],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003757679,0.00001277436,0.0006730847,0.0000388944,0.000005903092,0.0002581577,0.000269467,0.003050827,0.002732289,0.9801993,0.00085174,0.01187011],"study_design_scores_gemma":[0.00004817644,0.0001201905,0.002655206,0.00005667106,0.00002800668,0.001664202,0.0002846234,0.07340918,0.009099792,0.8914014,0.02116436,0.0000682777],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6844063,0.001717388,0.2369669,0.0009601159,0.00021986,0.00005891932,0.0002407495,0.0002769727,0.07515273],"genre_scores_gemma":[0.9619054,0.0006842172,0.02554245,0.0001538951,0.0001678894,0.00006077802,0.0001435308,0.00006689906,0.01127496],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003274201,"threshold_uncertainty_score":0.01095331,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2072839457","doi":"10.1090/s0002-9947-2013-05980-6","title":"New properties of multiple harmonic sums modulo 𝑝 and 𝑝-analogues of Leshchiner’s series","year":2013,"lang":"lv","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":67,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Saint Mary's University; Dalhousie University","funders":"","keywords":"Mathematics; Modulo; Series (stratigraphy); Harmonic; Pure mathematics; Arithmetic; Combinatorics","authors":[{"name":"Kh. Hessami Pilehrood","is_ca":true},{"name":"Tatiana Hessami Pilehrood","is_ca":true},{"name":"Roberto Tauraso","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03369017047511683,"gpt":0.2605702681690139,"spread":0.2268800976938971,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001169336,0.0005911018,0.0006312131,0.0024225,0.00183273,0.002626812,0.0009256269,0.0006318956,0.01432761],"category_scores_gemma":[0.003700832,0.0003494803,0.0007730279,0.001497498,0.002150959,0.004414776,0.001832519,0.002717018,0.002048589],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001209353,"about_ca_system_score_gemma":0.0004674114,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004423188,"about_ca_topic_score_gemma":0.0004661493,"domain_scores_codex":[0.9991922,0.0001138211,0.00004526023,0.0001479634,0.0003607733,0.0001399447],"domain_scores_gemma":[0.9989713,0.0003688804,0.0001775579,0.00009894508,0.0001921125,0.0001911459],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001961074,0.00001271599,0.0001695362,0.00004265802,0.00000577948,0.000148423,0.0002387995,0.0003323529,0.00101282,0.9856431,0.001523959,0.01085025],"study_design_scores_gemma":[0.00002071703,0.00004409105,0.0007466729,0.00003824819,0.00001687549,0.0006775602,0.0001873615,0.005336598,0.001929855,0.9660433,0.02492242,0.00003626962],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2965792,0.003978606,0.1737104,0.002517163,0.003067174,0.0001253474,0.0003680428,0.0004845432,0.5191694],"genre_scores_gemma":[0.8676812,0.002390651,0.03714096,0.0008035919,0.003585291,0.0001269924,0.0002947344,0.0003567395,0.0876199],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01432761,"threshold_uncertainty_score":0.04793066,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2025155363","doi":"10.2298/fil1404695s","title":"Some families of differential equations associated with the Hermite-based Appell polynomials and other classes of Hermite-based polynomials","year":2014,"lang":"en","type":"article","venue":"Filomat","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":64,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Hermite polynomials; Mathematics; Pure mathematics; Difference polynomials; Euler's formula; Hermite interpolation; Orthogonal polynomials; Algebra over a field; Mathematical analysis","authors":[{"name":"H. M. Srivastava","is_ca":true},{"name":"Mehmet Ali Özarslan","is_ca":false},{"name":"Banu Yılmaz","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03438518519909477,"gpt":0.2820275591287985,"spread":0.2476423739297037,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001005233,0.0006464747,0.0005002031,0.001633655,0.000947392,0.001109876,0.0006702259,0.0009031761,0.00394691],"category_scores_gemma":[0.002808744,0.000323662,0.001319814,0.001083113,0.001364104,0.00219178,0.001002755,0.002012471,0.0004923801],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001200329,"about_ca_system_score_gemma":0.0008064389,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002394598,"about_ca_topic_score_gemma":0.002201713,"domain_scores_codex":[0.9995481,0.0001276681,0.00002181404,0.00007859336,0.0001449933,0.00007876729],"domain_scores_gemma":[0.9993604,0.0002409769,0.0001239767,0.00004463809,0.0001638175,0.00006624444],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000009107308,0.00001201334,0.0003301889,0.0000408933,0.00001051877,0.0001223221,0.0002088579,0.005710339,0.00124478,0.9850971,0.0009359719,0.0062779],"study_design_scores_gemma":[0.00001892954,0.00003080713,0.0007992046,0.00003535614,0.00001766994,0.0006169723,0.0002154656,0.1734364,0.001016316,0.8143784,0.009388283,0.00004619823],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1129111,0.004282218,0.8187334,0.001980828,0.0004801739,0.0001156764,0.000477416,0.0001052682,0.06091381],"genre_scores_gemma":[0.8290783,0.006209568,0.1160714,0.0007184594,0.0007315375,0.0002465883,0.0005444868,0.0001191738,0.0462804],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00394691,"threshold_uncertainty_score":0.01320368,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2094244930","doi":"10.1007/s11139-005-3505-6","title":"Explicit Evaluation of Euler and Related Sums","year":2005,"lang":"en","type":"article","venue":"The Ramanujan Journal","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":62,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Euler's formula; Euler summation; Mathematics; Proof of the Euler product formula for the Riemann zeta function; Euler number (physics); Pure mathematics; Hypergeometric function; Semi-implicit Euler method; Hypergeometric distribution; Euler method; Applied mathematics; Backward Euler method; Euler equations; Mathematical analysis; Riemann hypothesis","authors":[{"name":"Junesang Choi","is_ca":false},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.09422361964570788,"gpt":0.3713147119237133,"spread":0.2770910922780054,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001768226,0.001086451,0.001155817,0.002512845,0.001958375,0.003795047,0.001598578,0.001235572,0.009464446],"category_scores_gemma":[0.006443103,0.0006085734,0.0006795465,0.001438383,0.003433895,0.007709379,0.003474881,0.002614707,0.00133665],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00172328,"about_ca_system_score_gemma":0.0008751333,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008299806,"about_ca_topic_score_gemma":0.001615432,"domain_scores_codex":[0.9989412,0.000315758,0.00005772573,0.0001142383,0.0003931217,0.0001778758],"domain_scores_gemma":[0.9986216,0.0005468678,0.0001166376,0.0002056881,0.0002979405,0.0002112387],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001901055,0.00002120539,0.0001054386,0.00003303961,0.000004444997,0.00007017182,0.0001757319,0.0007329349,0.0005098767,0.9941655,0.0006125564,0.003550012],"study_design_scores_gemma":[0.000008093431,0.000006092701,0.0001047927,0.00002185916,0.000006024298,0.00009766738,0.00005936369,0.006620333,0.0006978339,0.9899657,0.002398736,0.0000134325],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4267702,0.004902143,0.2013464,0.00368075,0.001741378,0.00007130878,0.000216514,0.0005629263,0.3607083],"genre_scores_gemma":[0.9061204,0.001427949,0.02971891,0.0003940461,0.000658983,0.00004433928,0.000150142,0.0003743581,0.06111081],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009464446,"threshold_uncertainty_score":0.03166169,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2029880297","doi":"10.1155/2007/19381","title":"Integer Powers of Arcsin","year":2007,"lang":"en","type":"article","venue":"International Journal of Mathematics and Mathematical Sciences","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":58,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Ramanujan's sum; Generalization; Inverse trigonometric functions; Integer (computer science); Simple (philosophy); Binomial coefficient; Trigonometric functions; Function (biology); Binomial (polynomial); Pure mathematics; Discrete mathematics; Combinatorics; Mathematical analysis; Statistics; Geometry","authors":[{"name":"Jonathan M. Borwein","is_ca":true},{"name":"Marc Chamberland","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.05366947006939587,"gpt":0.3913133740599157,"spread":0.3376439039905198,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004768917,0.0006913263,0.0004151175,0.001256324,0.0009844778,0.002301455,0.0006328844,0.000517575,0.0113815],"category_scores_gemma":[0.00180642,0.000214445,0.0003616493,0.0006727166,0.001775447,0.003657434,0.001021978,0.001318102,0.002037027],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006040881,"about_ca_system_score_gemma":0.0002989133,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000161906,"about_ca_topic_score_gemma":0.0002448537,"domain_scores_codex":[0.999699,0.00006523603,0.00001569166,0.00005763377,0.0001106603,0.00005169008],"domain_scores_gemma":[0.9996464,0.000106541,0.00004941571,0.00007321552,0.00006265992,0.0000616684],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00001539333,0.000009945752,0.0000591477,0.00002286198,0.000001330302,0.00005408374,0.00008027832,0.0004588009,0.001068819,0.9909667,0.000769862,0.006492781],"study_design_scores_gemma":[0.000006704166,0.00002129653,0.0001084083,0.00002924266,0.000006119164,0.0002829447,0.00007199887,0.007060926,0.002229965,0.974158,0.01600896,0.00001547356],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"other","genre_gemma":"methods","genre_scores_codex":[0.2506706,0.002308037,0.31318,0.001165421,0.001798091,0.00007918779,0.0002117852,0.0008752313,0.4297117],"genre_scores_gemma":[0.8988808,0.001024836,0.03654204,0.0003445347,0.0004882692,0.0000596125,0.0001130471,0.0002900446,0.06225681],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.0113815,"threshold_uncertainty_score":0.03807491,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1977710459","doi":"10.1016/j.camwa.2011.09.010","title":"Some series identities involving the generalized Apostol type and related polynomials","year":2011,"lang":"en","type":"article","venue":"Computers & Mathematics with Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":57,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Wilson polynomials; Difference polynomials; Classical orthogonal polynomials; Discrete orthogonal polynomials; Macdonald polynomials; Hahn polynomials; Orthogonal polynomials; Koornwinder polynomials; Pure mathematics; Gegenbauer polynomials; Combinatorics","authors":[{"name":"Da-Qian Lu","is_ca":false},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04949446309089626,"gpt":0.2791595427004343,"spread":0.2296650796095381,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001364053,0.0006623672,0.0007649573,0.001891018,0.001968122,0.002638902,0.0009082634,0.001356037,0.006312985],"category_scores_gemma":[0.003429619,0.0003300583,0.001113829,0.001921832,0.002796039,0.00428742,0.001464696,0.002583417,0.001231673],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001413584,"about_ca_system_score_gemma":0.000808625,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008962755,"about_ca_topic_score_gemma":0.0009785813,"domain_scores_codex":[0.9995198,0.0001312216,0.00002989915,0.00007936685,0.0001616367,0.00007798124],"domain_scores_gemma":[0.9992356,0.0002813335,0.0001192564,0.00009934772,0.0001601653,0.0001042814],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001046277,0.00001047579,0.000099956,0.00002287532,0.000003081819,0.00009291706,0.0001054184,0.0002947946,0.0002786485,0.9949096,0.001019059,0.003152856],"study_design_scores_gemma":[0.000008835069,0.000007785293,0.0001191176,0.000009205646,0.000005192215,0.0001622892,0.00004488795,0.002469985,0.0001885202,0.9933712,0.003603528,0.000009406765],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3167981,0.009299494,0.2732531,0.007323606,0.00352739,0.0001303645,0.0005033285,0.0002814165,0.3888832],"genre_scores_gemma":[0.8730229,0.004521737,0.04089745,0.001345766,0.003468844,0.0001052772,0.0002868434,0.0001405673,0.07621067],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006312985,"threshold_uncertainty_score":0.02111906,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2790728329","doi":"10.1007/jhep01(2019)155","title":"From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop","year":2019,"lang":"en","type":"article","venue":"Journal of High Energy Physics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":56,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Perimeter Institute","funders":"Hausdorff Research Institute for Mathematics; Agence Nationale de la Recherche","keywords":"Massless particle; Scattering amplitude; Modular design; Loop (graph theory); Generalization; Projection (relational algebra); Graph; Amplitude; String (physics)","authors":[],"retraction":null,"screen_n_in":null,"score":{"opus":0.03573979228471698,"gpt":0.2771764594880634,"spread":0.2414366672033464,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006363388,0.001224552,0.0005195349,0.003474316,0.001174924,0.00272651,0.001236632,0.001491866,0.004428338],"category_scores_gemma":[0.003205668,0.000464485,0.0006375305,0.001110207,0.004340146,0.004027414,0.002033825,0.002088666,0.0006042249],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007101785,"about_ca_system_score_gemma":0.0004065735,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004197521,"about_ca_topic_score_gemma":0.0004421683,"domain_scores_codex":[0.9997335,0.0000682032,0.000012079,0.00004670327,0.00007843637,0.00006108444],"domain_scores_gemma":[0.9988976,0.0004439789,0.0002164333,0.0001277249,0.00008786307,0.0002263426],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00007037305,0.00008883499,0.0009748371,0.00008241705,0.0000105466,0.0007171523,0.0008017808,0.005550504,0.009712384,0.9754059,0.0004389475,0.006146221],"study_design_scores_gemma":[0.00001647076,0.00002595208,0.001078578,0.00003398342,0.000007966318,0.0003761515,0.0002072502,0.04185478,0.002202988,0.9537106,0.0004580251,0.00002739301],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8754495,0.0005967726,0.07835875,0.000750963,0.0002058789,0.00003916809,0.00008010035,0.000395513,0.04412325],"genre_scores_gemma":[0.9902825,0.0002861888,0.004358084,0.0001121957,0.0001020652,0.00001901529,0.00004382014,0.0001003442,0.00469573],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004428338,"threshold_uncertainty_score":0.01481426,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1706478672","doi":"10.1007/978-4-431-54919-2_14","title":"Poly-Bernoulli Numbers","year":2014,"lang":"en","type":"book-chapter","venue":"Springer monographs in mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":52,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Bernoulli's principle; Mathematics; Physics; Thermodynamics","authors":[{"name":"Tomoyoshi Ibukiyama","is_ca":false},{"name":"Masanobu Kaneko","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04234883596280057,"gpt":0.2962770416082997,"spread":0.2539282056454991,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003757137,0.0009552781,0.000658297,0.001855903,0.00124462,0.003181576,0.0006885303,0.0007273122,0.03153249],"category_scores_gemma":[0.00138978,0.0003869602,0.0002919869,0.002358618,0.002210995,0.004221245,0.001602169,0.003704601,0.01379843],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001461953,"about_ca_system_score_gemma":0.0009452781,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000436589,"about_ca_topic_score_gemma":0.0006226974,"domain_scores_codex":[0.9995158,0.0001013257,0.00001906514,0.000081943,0.0002310728,0.00005087398],"domain_scores_gemma":[0.9996117,0.000142322,0.00003425194,0.00007247183,0.00008682042,0.00005249523],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005930879,0.000006607929,0.00002167731,0.00004343638,0.000001771353,0.0000134904,0.00004858371,0.000169366,0.0001607904,0.9591236,0.02168211,0.0187227],"study_design_scores_gemma":[0.0000032748,0.000006677471,0.00009930647,0.00007368381,0.000003431853,0.0001074835,0.00002996727,0.000664544,0.0002299938,0.6884483,0.3103249,0.000008456334],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.003211886,0.01419109,0.02913963,0.002414569,0.003920629,0.00002455552,0.0001960327,0.0001651613,0.9467365],"genre_scores_gemma":[0.09476116,0.0246635,0.01628464,0.001726037,0.005059865,0.0001381346,0.0004179133,0.0005082891,0.8564405],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.03153249,"threshold_uncertainty_score":0.1054867,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W273849276","doi":"10.1016/j.amc.2015.03.132","title":"Some new identities for the Apostol–Bernoulli polynomials and the Apostol–Genocchi polynomials","year":2015,"lang":"en","type":"article","venue":"Applied Mathematics and Computation","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":52,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"Kunming University of Science and Technology; Kunming Medical University; National Natural Science Foundation of China; National Science Foundation","keywords":"Mathematics; Classical orthogonal polynomials; Orthogonal polynomials; Discrete orthogonal polynomials; Wilson polynomials; Difference polynomials; Macdonald polynomials; Gegenbauer polynomials; Hahn polynomials; Pure mathematics","authors":[{"name":"Yuan He","is_ca":false},{"name":"Serkan Aracı","is_ca":false},{"name":"H. M. Srivastava","is_ca":true},{"name":"Mehmet Açıkgöz","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.07526031996793578,"gpt":0.3268006709013924,"spread":0.2515403509334566,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002084533,0.000929943,0.0007782065,0.003111831,0.002030599,0.002754115,0.001416138,0.001721684,0.007314392],"category_scores_gemma":[0.005593836,0.000505913,0.001183728,0.002331523,0.003803394,0.004826901,0.002578282,0.004466391,0.001966767],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001846957,"about_ca_system_score_gemma":0.001113932,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001002936,"about_ca_topic_score_gemma":0.001109007,"domain_scores_codex":[0.9992571,0.00020337,0.00005110392,0.0001150104,0.000265727,0.0001075977],"domain_scores_gemma":[0.9986967,0.0004591162,0.0001804628,0.0001388069,0.0002968569,0.0002280865],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000008046948,0.000008274214,0.00009394983,0.00003070159,0.000003120957,0.00006657258,0.0001262136,0.0002944129,0.0003456981,0.9928894,0.001559623,0.004574045],"study_design_scores_gemma":[0.000008307534,0.000009089839,0.0002127421,0.00001856335,0.000005226381,0.0001804371,0.00004343212,0.003432347,0.0002515482,0.9879571,0.007864628,0.00001670003],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1803072,0.01352448,0.4690458,0.01183715,0.008025204,0.0001754615,0.0008049758,0.0003579431,0.3159218],"genre_scores_gemma":[0.7738459,0.007943087,0.1103611,0.003137366,0.009403544,0.0002381306,0.0005819395,0.0003234394,0.09416553],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007314392,"threshold_uncertainty_score":0.02446908,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2963283179","doi":"10.4153/cjm-2002-016-9","title":"Mahler’s Measure and the Dilogarithm (I)","year":2002,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":52,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; Université de Bordeaux; National Science Foundation","keywords":"Mathematics; Quartic function; Measure (data warehouse); Dedekind cut; Cyclotomic field; Quadratic equation; Pure mathematics; Value (mathematics); Combinatorics; Discrete mathematics; Geometry; Statistics","authors":[{"name":"David W. Boyd","is_ca":true},{"name":"Fernando Rodriguez-Villegas","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.07013911650562334,"gpt":0.2578783560918545,"spread":0.1877392395862312,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005059639,0.0003273471,0.0003308604,0.002263326,0.0007679032,0.002117578,0.0006293859,0.0004811237,0.004735396],"category_scores_gemma":[0.001841717,0.0001426049,0.000238971,0.0007368255,0.002067563,0.001599391,0.0008652227,0.0007009606,0.000516938],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001552827,"about_ca_system_score_gemma":0.000241042,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006996278,"about_ca_topic_score_gemma":0.0006345039,"domain_scores_codex":[0.9997709,0.00004056347,0.00001171286,0.00003746616,0.00009027921,0.00004910437],"domain_scores_gemma":[0.9993625,0.0001948302,0.0001260541,0.00005394225,0.0001099129,0.0001527125],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001211424,0.000006349086,0.0004351474,0.00001216552,0.000003166813,0.00005237676,0.0000898878,0.0004860049,0.0006122122,0.9957933,0.0003771482,0.002120221],"study_design_scores_gemma":[0.00001093474,0.00002037097,0.001407397,0.00001491621,0.00000539299,0.000189679,0.0001063376,0.007948156,0.001007476,0.9861895,0.003078612,0.00002133907],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8414013,0.001381649,0.04443493,0.001819132,0.000202217,0.00002390094,0.0001956337,0.0002093286,0.1103319],"genre_scores_gemma":[0.99334,0.0001484672,0.001530781,0.00004647022,0.00008717655,0.000007509962,0.00003712363,0.00001544039,0.004787012],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004735396,"threshold_uncertainty_score":0.01584154,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1963748435","doi":"10.1007/s11139-014-9600-9","title":"A family of shifted harmonic sums","year":2014,"lang":"en","type":"article","venue":"The Ramanujan Journal","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":51,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Reciprocal; Harmonic number; Mathematics; Binomial coefficient; Euler's formula; Harmonic; Series (stratigraphy); Binomial (polynomial); Hypergeometric function; Basic hypergeometric series; Argument (complex analysis); Pure mathematics; Generalized hypergeometric function; Set (abstract data type); Hypergeometric identity; Hypergeometric distribution; Applied mathematics; Hypergeometric function of a matrix argument; Mathematical analysis; Discrete mathematics; Statistics; Computer science; Physics; Riemann hypothesis; Linguistics; Quantum mechanics","authors":[{"name":"Anthony Sofo","is_ca":false},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.0597080423263787,"gpt":0.3206468417464104,"spread":0.2609387994200317,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008235344,0.0008062568,0.0008563106,0.002372749,0.002329155,0.00282529,0.001496539,0.00138033,0.008977614],"category_scores_gemma":[0.002832617,0.0005873669,0.0008553271,0.001378258,0.002539696,0.003322927,0.002312472,0.002374524,0.00135996],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001162848,"about_ca_system_score_gemma":0.000655383,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005031504,"about_ca_topic_score_gemma":0.0003927295,"domain_scores_codex":[0.9993352,0.0001492364,0.00002994913,0.0001372489,0.0002399389,0.0001084602],"domain_scores_gemma":[0.9990877,0.0002817423,0.0001030519,0.0001192521,0.0001856872,0.0002225774],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001510228,0.000009774626,0.00008438805,0.00002243853,0.00000880761,0.00008938034,0.0001138724,0.0004851292,0.0009866033,0.993126,0.0006523344,0.004406089],"study_design_scores_gemma":[0.00001356229,0.00001569109,0.0002224127,0.00001765451,0.000009281887,0.0003510571,0.00006653996,0.007518314,0.0005375839,0.9861734,0.00505401,0.00002045723],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5130388,0.005086468,0.2562898,0.002941824,0.001453309,0.00008962712,0.000299925,0.0005153531,0.2202849],"genre_scores_gemma":[0.894582,0.002202343,0.02700133,0.0008355323,0.001058038,0.0001248657,0.0002583734,0.0002640978,0.0736734],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008977614,"threshold_uncertainty_score":0.03003311,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2056308826","doi":"10.4064/aa124-2-4","title":"On the two-dimensional theta functions of the Borweins","year":2006,"lang":"en","type":"article","venue":"Acta Arithmetica","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":51,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Pure mathematics; Algebra over a field","authors":[{"name":"Ayşe Alaca","is_ca":true},{"name":"Şaban Alaca","is_ca":true},{"name":"Kenneth S. Williams","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02626458730869688,"gpt":0.2806634861240655,"spread":0.2543988988153686,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00200625,0.001189407,0.001082456,0.002748281,0.002607135,0.003924846,0.001214761,0.001417382,0.007242028],"category_scores_gemma":[0.003271765,0.0005545954,0.0008199302,0.002010773,0.005985551,0.005319989,0.002784658,0.003477598,0.00170068],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001702477,"about_ca_system_score_gemma":0.0008542056,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001300128,"about_ca_topic_score_gemma":0.0007456932,"domain_scores_codex":[0.9993773,0.0002315041,0.00003503082,0.00008237651,0.0001380167,0.0001358369],"domain_scores_gemma":[0.9993103,0.0002215718,0.0001029513,0.00008992919,0.00009670038,0.0001786039],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001514417,0.000005095907,0.00005275034,0.000007711009,0.000001692466,0.00001739009,0.0001350401,0.0001752896,0.0001369819,0.9975311,0.0003716942,0.001550226],"study_design_scores_gemma":[0.0000151023,0.000008165311,0.00009174235,0.000009865913,0.000002587876,0.00003942017,0.00008296495,0.001150139,0.0001011909,0.9964896,0.002001103,0.000008033278],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5171995,0.005926447,0.1146618,0.0081084,0.002203665,0.00008120449,0.0002952817,0.0003720467,0.3511515],"genre_scores_gemma":[0.9317614,0.00243983,0.01718586,0.0008157381,0.001082587,0.00009498115,0.0001330146,0.0001856187,0.04630098],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007242028,"threshold_uncertainty_score":0.02422696,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1964935995","doi":"10.1016/j.jmaa.2005.04.040","title":"Parametric Euler sum identities","year":2005,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":46,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Dalhousie University; Western University","funders":"","keywords":"Mathematics; Meromorphic function; Euler's formula; Parametric statistics; Pure mathematics; Reduction (mathematics); Applied mathematics; Algebra over a field; Mathematical analysis; Statistics; Geometry","authors":[{"name":"David Borwein","is_ca":true},{"name":"Jonathan M. Borwein","is_ca":true},{"name":"David M. Bradley","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03277565124453563,"gpt":0.3362618914653837,"spread":0.3034862402208481,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007313594,0.0009172995,0.0008939208,0.002214981,0.001992123,0.003459571,0.0008998995,0.001085898,0.0155719],"category_scores_gemma":[0.002024432,0.000466834,0.0007686063,0.001272519,0.002168766,0.007091807,0.00306946,0.003853897,0.003424953],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009564625,"about_ca_system_score_gemma":0.0005968767,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003713054,"about_ca_topic_score_gemma":0.0003308491,"domain_scores_codex":[0.9994897,0.00009343073,0.0000276985,0.00008678466,0.0002394858,0.00006297488],"domain_scores_gemma":[0.9994143,0.0001259036,0.00006357275,0.0001270705,0.0001780943,0.00009102668],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000002331014,0.000004129214,0.00002321469,0.000006437664,0.000001602131,0.00001346489,0.00004686143,0.00007338603,0.0001099222,0.9964734,0.001121672,0.002123588],"study_design_scores_gemma":[0.000001429087,0.000002414179,0.00005080496,0.000005876157,0.000003647155,0.00009619872,0.00002595985,0.0006297583,0.0001435075,0.9919337,0.007102245,0.000004442397],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.08499482,0.002759311,0.1797792,0.005600967,0.002932162,0.00004586131,0.0004246655,0.0004079044,0.7230552],"genre_scores_gemma":[0.709076,0.002905769,0.0269133,0.0009890386,0.002368603,0.00008122264,0.0004597615,0.0004516779,0.2567547],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0155719,"threshold_uncertainty_score":0.05209315,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1983635056","doi":"10.1093/imrn/rns285","title":"On the Mahler Measure of 1+X+1/X+Y +1/Y","year":2013,"lang":"en","type":"article","venue":"International Mathematics Research Notices","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":43,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Université de Montréal","funders":"","keywords":"Measure (data warehouse); Mathematics; Volume (thermodynamics); Library science; Computer science; Physics; Database","authors":[{"name":"Mathew D. Rogers","is_ca":true},{"name":"Wadim Zudilin","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.2940428648331191,"gpt":0.4679977798485687,"spread":0.1739549150154496,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001639124,0.0009299346,0.001143188,0.004020793,0.00187015,0.003705001,0.002026161,0.001775025,0.008170808],"category_scores_gemma":[0.008988253,0.0004031444,0.000965277,0.002008873,0.005425454,0.006412625,0.002986254,0.00341663,0.001267322],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001905699,"about_ca_system_score_gemma":0.0005994422,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005762727,"about_ca_topic_score_gemma":0.0003181515,"domain_scores_codex":[0.9991482,0.000186426,0.00003872091,0.0001805624,0.0002832082,0.0001627806],"domain_scores_gemma":[0.9965133,0.001872711,0.000594493,0.0002348823,0.0003174087,0.0004672673],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001823055,0.000009897893,0.0003607717,0.00003118146,0.000006008329,0.00006052807,0.0001349565,0.0004397299,0.0006249644,0.995766,0.0005510118,0.001996708],"study_design_scores_gemma":[0.00001194252,0.00003662133,0.0006046293,0.00003417203,0.000009758292,0.0002319188,0.00007977428,0.004260816,0.0008342309,0.9918721,0.001995373,0.0000286211],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6612158,0.003547931,0.1874426,0.007445199,0.001497572,0.0000597178,0.000443074,0.000504273,0.1378438],"genre_scores_gemma":[0.9784177,0.0009614979,0.008634879,0.0005598455,0.001356964,0.00006562517,0.0001607026,0.0001361796,0.009706628],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008170808,"threshold_uncertainty_score":0.02733409,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2044773284","doi":"10.1080/10586458.2008.10129026","title":"The 2-adic Valuation of Stirling Numbers","year":2008,"lang":"en","type":"article","venue":"Experimental Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":43,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Dalhousie University","funders":"National Science Foundation","keywords":"Mathematics; Conjecture; Valuation (finance); Stirling numbers of the second kind; Stirling number; Stirling engine; Stirling numbers of the first kind; Combinatorics; Discrete mathematics; Pure mathematics; Thermodynamics","authors":[{"name":"Tewodros Amdeberhan","is_ca":false},{"name":"Dante Manna","is_ca":true},{"name":"Victor H. Moll","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.1376574225503683,"gpt":0.3734146719359994,"spread":0.2357572493856311,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001265098,0.0007359536,0.0005723403,0.003584565,0.001121344,0.004617221,0.0005113157,0.0006746488,0.006472467],"category_scores_gemma":[0.003750559,0.0003239101,0.0005534759,0.001635058,0.003321703,0.004609629,0.001041207,0.001200455,0.000741896],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001138755,"about_ca_system_score_gemma":0.0004999862,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002623614,"about_ca_topic_score_gemma":0.0001955751,"domain_scores_codex":[0.999523,0.0001156905,0.00002503002,0.00007457677,0.0001502988,0.0001114136],"domain_scores_gemma":[0.9984359,0.0007120408,0.0003126842,0.0001224392,0.0001973695,0.0002195931],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002409011,0.000008891904,0.0002634585,0.00003159656,0.000003581495,0.00007079978,0.00008697282,0.0007265689,0.0009030855,0.9957232,0.0003112791,0.001846408],"study_design_scores_gemma":[0.00001876189,0.00003935492,0.0007748365,0.00003768874,0.00000988421,0.0004166306,0.0001220059,0.006116381,0.001218023,0.9874259,0.003794343,0.0000262472],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7524088,0.003216694,0.04723068,0.00104303,0.0005656478,0.00004726719,0.0002490237,0.0001235459,0.1951153],"genre_scores_gemma":[0.9884758,0.0006742133,0.003446046,0.00009122474,0.0002939106,0.00002540393,0.00007119247,0.0000238722,0.006898274],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006472467,"threshold_uncertainty_score":0.02165258,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1999307238","doi":"10.1073/pnas.0237168100","title":"The Euler–Maclaurin formula for simple integral polytopes","year":2003,"lang":"en","type":"article","venue":"Proceedings of the National Academy of Sciences","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":43,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Toronto","funders":"","keywords":"Polytope; Simple (philosophy); Euler's formula; Mathematics; Applied mathematics; Mathematical analysis; Combinatorics; Philosophy","authors":[{"name":"Yael Karshon","is_ca":true},{"name":"Shlomo Sternberg","is_ca":true},{"name":"Jonathan Weitsman","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.0973054161219526,"gpt":0.3825113720606524,"spread":0.2852059559386999,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000647692,0.0009477184,0.000705993,0.001673025,0.001081459,0.002150931,0.0009773769,0.0007078002,0.00644546],"category_scores_gemma":[0.001730389,0.0003674471,0.0007289894,0.001040174,0.002210598,0.003328157,0.001862604,0.002375024,0.001364114],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008299236,"about_ca_system_score_gemma":0.000385935,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004673472,"about_ca_topic_score_gemma":0.0004738509,"domain_scores_codex":[0.9996771,0.00003838201,0.00001940344,0.00005130064,0.0001578966,0.00005593893],"domain_scores_gemma":[0.9996033,0.0001163366,0.00006189081,0.00005615132,0.00008988885,0.00007256672],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002087468,0.00001992267,0.0002441742,0.00006412767,0.00000691269,0.000176521,0.000126929,0.003461586,0.002454256,0.9823132,0.001085224,0.01002642],"study_design_scores_gemma":[0.00001738459,0.00003816837,0.0004229891,0.00004247089,0.00001678766,0.0005056578,0.00008193991,0.02322552,0.004268944,0.9616289,0.009723444,0.00002776906],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2831909,0.002186444,0.5362743,0.001546734,0.0007718199,0.0000812196,0.0002837967,0.0004953327,0.1751695],"genre_scores_gemma":[0.8671852,0.001868325,0.09248376,0.0003423046,0.0004837586,0.00009021349,0.0002260713,0.0002475597,0.03707268],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00644546,"threshold_uncertainty_score":0.02156222,"prediction_status":"machine_predicted_unvalidated"},"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,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Mount Allison University","funders":"","keywords":"Mathematics; Congruence relation; Combinatorics; Pure mathematics; Arithmetic","authors":[{"name":"Heng Huat Chan","is_ca":false},{"name":"S. Barry Cooper","is_ca":false},{"name":"Francesco Sica","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.01467601782389216,"gpt":0.3456057596385875,"spread":0.3309297418146953,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003395426,0.0006264251,0.000868022,0.001502,0.002780843,0.003575426,0.0005880111,0.001087805,0.004174288],"category_scores_gemma":[0.009990934,0.000390616,0.001001726,0.001140604,0.004477098,0.005502337,0.002366531,0.00204684,0.0006344864],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001071772,"about_ca_system_score_gemma":0.0007918955,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005627946,"about_ca_topic_score_gemma":0.0003851846,"domain_scores_codex":[0.995603,0.0008831608,0.00044528,0.0007182272,0.00166864,0.0006818],"domain_scores_gemma":[0.995465,0.001824472,0.0008075243,0.0003896733,0.0008876399,0.0006257185],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00006150786,0.00002336566,0.000503439,0.00003378095,0.000008304764,0.0003952583,0.0003805253,0.0003709437,0.002922711,0.9928491,0.0003970402,0.002054016],"study_design_scores_gemma":[0.00006340732,0.00008185438,0.000587468,0.0000200038,0.00001056192,0.0004728172,0.000411775,0.003437925,0.002248577,0.9878047,0.00483192,0.00002907521],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7088094,0.001208766,0.1555732,0.001687643,0.00143113,0.00018603,0.0003253732,0.0002174843,0.1305609],"genre_scores_gemma":[0.9720491,0.0004176337,0.01772836,0.0002227326,0.0006793948,0.0001213508,0.0002281129,0.00007685273,0.008476389],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004174288,"threshold_uncertainty_score":0.01795691,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2091771439","doi":"10.1007/s00010-005-2774-x","title":"Evaluations of binomial series","year":2005,"lang":"en","type":"article","venue":"Aequationes Mathematicae","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":41,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Dalhousie University","funders":"","keywords":"Mathematics; Binomial coefficient; Combinatorics; Series (stratigraphy); Binomial (polynomial); Recursion (computer science); Algorithm; Statistics","authors":[{"name":"Jonathan M. Borwein","is_ca":true},{"name":"Roland Girgensohn","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.08443598403481739,"gpt":0.386079231913791,"spread":0.3016432478789736,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002423767,0.001006731,0.001069741,0.004303137,0.002240181,0.006825274,0.00127877,0.0009498644,0.01637634],"category_scores_gemma":[0.01185109,0.0005417768,0.0006931713,0.002047299,0.003344618,0.005365682,0.002691125,0.002816912,0.002613137],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002582479,"about_ca_system_score_gemma":0.0008629757,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008640605,"about_ca_topic_score_gemma":0.0008510225,"domain_scores_codex":[0.9981719,0.0005070097,0.0000734386,0.0002399624,0.000670597,0.0003370838],"domain_scores_gemma":[0.9971862,0.001129493,0.0002356297,0.0002097421,0.0007501461,0.0004887764],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003903775,0.00001644632,0.0002652858,0.00002891405,0.000007199033,0.00008389681,0.0001709873,0.0005054252,0.0005300051,0.9892799,0.001711271,0.007361806],"study_design_scores_gemma":[0.00001336505,0.00001534225,0.0003694508,0.00003072215,0.00001164965,0.0002141184,0.00008816546,0.005021141,0.0006880719,0.9878737,0.005658235,0.00001612582],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3005846,0.003706588,0.1550208,0.003454501,0.001742172,0.00008643656,0.0003825511,0.0005375489,0.5344847],"genre_scores_gemma":[0.8937656,0.001701144,0.01648721,0.0003278959,0.001041468,0.00007257376,0.0003336805,0.0003128065,0.08595759],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01637634,"threshold_uncertainty_score":0.05478436,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2096646970","doi":"10.1017/s0004972700038661","title":"Evaluation of two convolution sums involving the sum of divisors function","year":2006,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":40,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Convolution (computer science); Function (biology); Convolution power; Pure mathematics; Mathematical analysis; Fourier transform","authors":[{"name":"Mathieu F. Lemire","is_ca":true},{"name":"Kenneth S. Williams","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.0742963986717339,"gpt":0.3275857208961128,"spread":0.2532893222243788,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002127061,0.001057277,0.001012834,0.001687553,0.001105796,0.004017985,0.001034654,0.0009721979,0.008471911],"category_scores_gemma":[0.007080534,0.0002960793,0.0008738734,0.001107754,0.002322786,0.003520632,0.002296846,0.001298753,0.001703019],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001578978,"about_ca_system_score_gemma":0.001390761,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005668949,"about_ca_topic_score_gemma":0.0007613552,"domain_scores_codex":[0.9980354,0.0003217825,0.0001187146,0.0001789734,0.0009985588,0.0003466392],"domain_scores_gemma":[0.9980425,0.0006280431,0.0001559596,0.0003010337,0.0006127607,0.000259681],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0006503299,0.0001486287,0.002967302,0.0004318757,0.0001181043,0.001923826,0.0009388147,0.007702208,0.0358966,0.8331736,0.005612003,0.1104367],"study_design_scores_gemma":[0.00007194366,0.0002543713,0.005657741,0.0002449987,0.0001573629,0.004188349,0.0005686907,0.1349281,0.09814365,0.7130923,0.04246713,0.0002253646],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2679265,0.001773789,0.5591264,0.000905456,0.001817376,0.0001414895,0.0002669325,0.001158672,0.1668833],"genre_scores_gemma":[0.7549295,0.0007983908,0.1795544,0.0003560109,0.000455962,0.0001197659,0.0004757651,0.001116402,0.06219373],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008471911,"threshold_uncertainty_score":0.02834135,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2605392197","doi":"10.1088/1751-8121/aac601","title":"Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes","year":2018,"lang":"en","type":"article","venue":"Journal of Physics A Mathematical and Theoretical","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":37,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"","funders":"Institut Périmètre de physique théorique; Deutsche Forschungsgemeinschaft","keywords":"Elliptic curve; Context (archaeology); Degenerate energy levels; Quarter period; Generalization; Rational number; Iterated function; Zeta function regularization","authors":[],"retraction":null,"screen_n_in":null,"score":{"opus":0.04740165551134929,"gpt":0.3288502622317094,"spread":0.2814486067203601,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006212282,0.000766887,0.0006267256,0.00207266,0.0009566502,0.002171804,0.0009490548,0.0009512968,0.003462456],"category_scores_gemma":[0.002780088,0.000286106,0.000531437,0.0007916745,0.003054365,0.002968247,0.001785008,0.001380868,0.0003227164],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006333738,"about_ca_system_score_gemma":0.0003931104,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002678835,"about_ca_topic_score_gemma":0.0002544372,"domain_scores_codex":[0.9997025,0.00006921685,0.00001866798,0.00003644794,0.0001101378,0.00006298733],"domain_scores_gemma":[0.9992669,0.0002145202,0.0001295535,0.00009000269,0.000125297,0.000173613],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00009472494,0.0000622798,0.001370237,0.00006853889,0.00002024385,0.001560774,0.0003624926,0.009914548,0.01066879,0.9696187,0.0003410892,0.005917524],"study_design_scores_gemma":[0.00003240735,0.00006778677,0.001255655,0.00004605117,0.00001774391,0.001130589,0.0005186014,0.1055781,0.006581347,0.8840287,0.0006995903,0.00004352617],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9181664,0.0002383787,0.04162578,0.0004015843,0.0001170017,0.00003056612,0.00002859269,0.0001349026,0.03925681],"genre_scores_gemma":[0.9949173,0.00009442602,0.002276304,0.00003610919,0.00003557474,0.00001259916,0.00001822787,0.00002908314,0.002580493],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003462456,"threshold_uncertainty_score":0.01158309,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1491845640","doi":"","title":"Zeros of Ramanujan Polynomials","year":2011,"lang":"en","type":"article","venue":"Edinburgh Research Explorer","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":37,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Ramanujan's sum; Mathematics; Unit circle; Combinatorics; Orthogonal polynomials; Reciprocal; Limiting; Pure mathematics; Discrete mathematics","authors":[{"name":"Christopher Smyth","is_ca":false},{"name":"Ram Murty","is_ca":false},{"name":"Rob Wang","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.5926673725483798,"gpt":0.4750510254041031,"spread":0.1176163471442767,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001649884,0.0005044146,0.0006583312,0.002043467,0.001369719,0.001724347,0.001011285,0.0005617263,0.004261922],"category_scores_gemma":[0.01264441,0.0004197543,0.0004154217,0.0008358104,0.002768276,0.002967814,0.001117111,0.00115679,0.0006483977],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000866061,"about_ca_system_score_gemma":0.0005683042,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006109518,"about_ca_topic_score_gemma":0.0002661937,"domain_scores_codex":[0.9988293,0.0004114718,0.00003992047,0.0002072425,0.0003107285,0.0002013089],"domain_scores_gemma":[0.994186,0.003641393,0.0007132115,0.0005117818,0.0006234467,0.0003241587],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001479779,0.00003422725,0.001199864,0.0001278621,0.00001693677,0.0001477488,0.000399118,0.01322702,0.01092802,0.9632175,0.0005669155,0.009986899],"study_design_scores_gemma":[0.00006665309,0.0001729567,0.001997847,0.00008455064,0.00002264217,0.0009094551,0.0004876474,0.1632968,0.01441862,0.8132801,0.005145389,0.0001173623],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7901218,0.001316686,0.1776375,0.000755788,0.00009069491,0.00004795297,0.0001638923,0.0002081316,0.02965747],"genre_scores_gemma":[0.989134,0.0003641345,0.007833209,0.00005213135,0.00008060027,0.00003395983,0.00006245425,0.00003788555,0.002401506],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004261922,"threshold_uncertainty_score":0.01425749,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2073512213","doi":"10.1016/j.aml.2011.05.012","title":"A new class of generalized Apostol–Bernoulli polynomials and some analogues of the Srivastava–Pintér addition theorem","year":2011,"lang":"en","type":"article","venue":"Applied Mathematics Letters","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":36,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Royal Military College of Canada; Université du Québec à Chicoutimi","funders":"","keywords":"Mathematics; Generalization; Class (philosophy); Difference polynomials; Orthogonal polynomials; Classical orthogonal polynomials; Pure mathematics; Discrete orthogonal polynomials; Algebra over a field; Discrete mathematics; Combinatorics; Mathematical analysis","authors":[{"name":"Richard E. Tremblay","is_ca":true},{"name":"Sébastien Gaboury","is_ca":true},{"name":"B.-J. Fugère","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04277310894971314,"gpt":0.2558574621268116,"spread":0.2130843531770985,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007593547,0.0006961179,0.0007611049,0.001987415,0.001450221,0.002289454,0.001136667,0.0009329591,0.006977761],"category_scores_gemma":[0.002348837,0.0003394441,0.0007547339,0.002061711,0.002231096,0.003289046,0.001553686,0.002364618,0.001091456],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006709229,"about_ca_system_score_gemma":0.0006760854,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003119115,"about_ca_topic_score_gemma":0.0003121185,"domain_scores_codex":[0.999548,0.00009559589,0.00002112928,0.0001090464,0.0001458824,0.00008043703],"domain_scores_gemma":[0.999158,0.0002276877,0.0001822642,0.0001152999,0.000150477,0.0001663151],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001649223,0.000008145636,0.0001168155,0.00003199717,0.000006058295,0.0001236668,0.00006126316,0.0004079222,0.001007442,0.9903092,0.001066091,0.006844875],"study_design_scores_gemma":[0.00001879802,0.00002506495,0.0003755446,0.00001575568,0.000009774119,0.0007865865,0.00004909454,0.006477288,0.00076133,0.9763021,0.01515154,0.00002709947],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.3896244,0.006294321,0.3232324,0.004021224,0.00274389,0.0001564575,0.0006553624,0.0005579398,0.272714],"genre_scores_gemma":[0.9033944,0.002771946,0.0412593,0.0008789618,0.002377243,0.0001045742,0.0003238417,0.0001497502,0.04873991],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006977761,"threshold_uncertainty_score":0.02334297,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2015374678","doi":"10.1016/j.camwa.2006.02.003","title":"Explicit formulas for the Nörlund polynomials Bn(χ) and bn(χ)","year":2006,"lang":"en","type":"article","venue":"Computers & Mathematics with Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":36,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Stirling numbers of the first kind; Stirling number; Stirling numbers of the second kind; Bernoulli number; Bell polynomials; Bernoulli polynomials; Polynomial; Discrete mathematics; Combinatorics; Pure mathematics; Algebra over a field; Difference polynomials; Orthogonal polynomials; Mathematical analysis","authors":[{"name":"Guodong Liu","is_ca":false},{"name":"H. M. Srivastava","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.029829485865797,"gpt":0.2975324516571932,"spread":0.2677029657913962,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001312479,0.0009522031,0.000552381,0.002038888,0.001214316,0.003026558,0.001558618,0.001325117,0.01111523],"category_scores_gemma":[0.005337749,0.0004135405,0.0004588571,0.001799794,0.002048876,0.005832203,0.002202037,0.003881494,0.002141126],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001647165,"about_ca_system_score_gemma":0.000994259,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009942889,"about_ca_topic_score_gemma":0.002115415,"domain_scores_codex":[0.9994656,0.00009379658,0.00003314134,0.00007541059,0.0002366747,0.00009539894],"domain_scores_gemma":[0.9989924,0.0003544793,0.0001071613,0.0001008822,0.0002883958,0.0001566129],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001596094,0.00001583982,0.00009448259,0.00003175563,0.000001756247,0.00004880576,0.0001554429,0.0002841261,0.0005021272,0.9889178,0.001003865,0.008928041],"study_design_scores_gemma":[0.00001195171,0.000007576535,0.0001456008,0.00003724059,0.000004293572,0.0001336118,0.00008276728,0.005408577,0.0007613251,0.9863745,0.007015846,0.00001680603],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1448022,0.004394186,0.6066893,0.004187934,0.001872539,0.0001220364,0.0007317513,0.0005430896,0.236657],"genre_scores_gemma":[0.7293344,0.003657125,0.1910356,0.001009196,0.000675812,0.000158307,0.0006353735,0.0004140721,0.07308025],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01111523,"threshold_uncertainty_score":0.03718412,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2735034614","doi":"10.1016/j.jnt.2017.05.008","title":"Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials","year":2017,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":35,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Fibonacci polynomials; Discrete orthogonal polynomials; Stirling number; Difference polynomials; Classical orthogonal polynomials; Orthogonal polynomials; Pure mathematics; Wilson polynomials; Hahn polynomials; Generating function; Discrete mathematics; Gegenbauer polynomials","authors":[{"name":"H. M. Srivastava","is_ca":true},{"name":"İrem Küçükoğlu","is_ca":false},{"name":"Yılmaz Şimşek","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.08058831837824938,"gpt":0.3689935840425959,"spread":0.2884052656643465,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00150765,0.0007594889,0.0009668312,0.001990837,0.001607995,0.002651378,0.001192252,0.00133985,0.003893661],"category_scores_gemma":[0.003909769,0.000417588,0.001292889,0.001314646,0.003004304,0.005171052,0.001924421,0.003257933,0.0006013766],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001833532,"about_ca_system_score_gemma":0.001285447,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001077401,"about_ca_topic_score_gemma":0.001831979,"domain_scores_codex":[0.9994703,0.0001345386,0.00003269655,0.0001005621,0.0001822818,0.00007963821],"domain_scores_gemma":[0.9989758,0.0003355349,0.0001734256,0.00009323454,0.0002357407,0.0001862797],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000004381763,0.000005809695,0.00008115046,0.00001019208,0.000003030002,0.00005292646,0.00006476039,0.0006957403,0.000297709,0.9965994,0.0004003072,0.001784661],"study_design_scores_gemma":[0.0000140332,0.00001117792,0.0001396719,0.00001174472,0.000004658132,0.0002125681,0.0000479449,0.01956909,0.0001611299,0.9755312,0.004279506,0.00001731495],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1805584,0.004183506,0.6889423,0.007165574,0.002542261,0.000107715,0.0005126778,0.0001727062,0.1158149],"genre_scores_gemma":[0.8032356,0.003909978,0.1195611,0.001534467,0.002669456,0.0002044651,0.000390467,0.0001610508,0.06833341],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003893661,"threshold_uncertainty_score":0.01330322,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2068789747","doi":"10.1016/j.jmaa.2007.10.011","title":"Ramanujan's series for <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">/</mml:mo> <mml:mi>π</mml:mi> </mml:math> arising from his cubic and quartic theories of elliptic functions","year":2007,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":35,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"","funders":"Department of Science and Technology, Ministry of Science and Technology, India; National Sanitarium Association","keywords":"Series (stratigraphy); Mathematics; Ramanujan's sum; Scroll; Philosophy; Combinatorics; Theology; Geology","authors":[{"name":"Nayandeep Deka Baruah","is_ca":false},{"name":"Bruce C. Berndt","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.01890114914219718,"gpt":0.2703768311891218,"spread":0.2514756820469246,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001229196,0.001225287,0.0009208487,0.003640852,0.002334341,0.003759217,0.001304442,0.001146304,0.03288184],"category_scores_gemma":[0.003765074,0.0003772312,0.001129969,0.002256903,0.00250689,0.003593814,0.001706629,0.005798297,0.01055307],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002311614,"about_ca_system_score_gemma":0.001405148,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001392234,"about_ca_topic_score_gemma":0.001880247,"domain_scores_codex":[0.9992932,0.0001737479,0.00003035182,0.0001008013,0.0003203137,0.00008148007],"domain_scores_gemma":[0.9988972,0.0003825437,0.00009941794,0.0001911179,0.0002936434,0.0001360578],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000007707657,0.0000125658,0.0000560253,0.00004707848,0.000008971891,0.00005211034,0.0001658484,0.0003564576,0.00037587,0.9721373,0.01196077,0.01481921],"study_design_scores_gemma":[0.000009427486,0.00001271134,0.0002842366,0.00003909989,0.000007800336,0.000181576,0.00006760244,0.002389753,0.0002980325,0.9461756,0.05051373,0.00002046267],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.03501432,0.01845718,0.1100083,0.01110929,0.00875603,0.0000912428,0.0006269303,0.0005686735,0.8153681],"genre_scores_gemma":[0.4338693,0.02132002,0.07701027,0.002524602,0.007077934,0.000308122,0.0007496006,0.0009382925,0.4562018],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.03288184,"threshold_uncertainty_score":0.1100007,"prediction_status":"machine_predicted_unvalidated"},"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,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"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","authors":[],"retraction":null,"screen_n_in":null,"score":{"opus":0.02219150538033221,"gpt":0.3536649628456861,"spread":0.3314734574653539,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008716247,0.0006419407,0.0004428867,0.00142639,0.00189896,0.002236782,0.000847579,0.0006854871,0.009962279],"category_scores_gemma":[0.001980777,0.0002550531,0.0004835166,0.0009427637,0.004188693,0.002287009,0.003549995,0.001429325,0.002068925],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00172725,"about_ca_system_score_gemma":0.0007286109,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006592061,"about_ca_topic_score_gemma":0.0007472524,"domain_scores_codex":[0.9993901,0.0001108129,0.00003906158,0.00009962117,0.0002460182,0.0001142923],"domain_scores_gemma":[0.9996182,0.0001202078,0.00003794372,0.00007020867,0.00007690519,0.00007657213],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005650508,0.00000180195,0.00004140034,0.00002004034,0.000001870258,0.00002585014,0.00008727086,0.0001691285,0.0002291733,0.993642,0.0008937661,0.00488213],"study_design_scores_gemma":[0.00000838533,0.00001373002,0.0002002778,0.00003831204,0.00000550657,0.0001233944,0.0001089066,0.0008715581,0.0009893818,0.95465,0.04297239,0.00001803047],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.1965914,0.006637026,0.1045993,0.00619395,0.002303995,0.0001255925,0.0004998447,0.0006816852,0.6823673],"genre_scores_gemma":[0.8938221,0.003006371,0.02810327,0.0008037043,0.0005494635,0.00009078126,0.0001930965,0.0001599227,0.07327121],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009962279,"threshold_uncertainty_score":0.03332716,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W3105552015","doi":"","title":"Integral and Series Representations of Riemann’s Zeta Function and Dirichlet’s Eta Function and a Medley of Related Results","year":2016,"lang":"en","type":"article","venue":"","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":34,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Ducks Unlimited Canada","funders":"","keywords":"Riemann zeta function; Mathematics; Dirichlet series; Riemann hypothesis; Series (stratigraphy); Arithmetic zeta function; Function (biology); Dirichlet eta function; Dirichlet L-function; Particular values of Riemann zeta function; General Dirichlet series; Pure mathematics; Mathematical analysis; Explicit formulae; Dirichlet distribution; Prime zeta function; Calculus (dental)","authors":[{"name":"Michael Milgram","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03329707386127455,"gpt":0.2983636278361627,"spread":0.2650665539748881,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001366076,0.001105955,0.000741365,0.003503084,0.001151377,0.00416292,0.0009813673,0.001262521,0.009619209],"category_scores_gemma":[0.00517189,0.0002542536,0.001162525,0.002444676,0.002882463,0.007383099,0.00194558,0.003129474,0.002288089],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001268184,"about_ca_system_score_gemma":0.0006376578,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004407962,"about_ca_topic_score_gemma":0.0002569175,"domain_scores_codex":[0.9993854,0.0001542521,0.00003783981,0.00009032361,0.0002738121,0.0000584316],"domain_scores_gemma":[0.9990068,0.0003776747,0.0001201329,0.000151547,0.0002560112,0.00008783607],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000003487778,0.000009154312,0.00004086932,0.00002301911,0.000001691889,0.00002427686,0.00008814011,0.000407229,0.0002023735,0.9934701,0.0009363034,0.004793398],"study_design_scores_gemma":[0.00000153963,0.000008881682,0.00009007971,0.00003648515,0.000003891163,0.0001354939,0.00008527566,0.004234934,0.0002259267,0.9865622,0.008607614,0.000007612521],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07398122,0.01927485,0.512114,0.004964992,0.003809059,0.00007127983,0.0002781124,0.0003364381,0.38517],"genre_scores_gemma":[0.6938169,0.02026929,0.1216842,0.001783862,0.005155537,0.000182984,0.0005759252,0.0004652035,0.156066],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009619209,"threshold_uncertainty_score":0.03217947,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2149824583","doi":"10.1016/j.disc.2008.01.030","title":"Shortened recurrence relations for Bernoulli numbers","year":2008,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":33,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Bernoulli number; Mathematics; Stirling numbers of the first kind; Recurrence relation; Stirling number; Stirling numbers of the second kind; Bernoulli's principle; Combinatorics; Bernoulli polynomials; Discrete mathematics; Bernoulli process","authors":[{"name":"Takashi Agoh","is_ca":false},{"name":"Karl Dilcher","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.0917419491776357,"gpt":0.3525544244270336,"spread":0.2608124752493979,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002014272,0.0008782299,0.000784096,0.002937219,0.001353596,0.002345906,0.001235704,0.0009881011,0.009488428],"category_scores_gemma":[0.007031997,0.0004966988,0.0007769676,0.002263339,0.001747041,0.003853071,0.001365142,0.002595866,0.002643074],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001679727,"about_ca_system_score_gemma":0.0007820983,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001509345,"about_ca_topic_score_gemma":0.001908372,"domain_scores_codex":[0.9988245,0.000342451,0.0001186122,0.0001684273,0.0004113902,0.0001345518],"domain_scores_gemma":[0.997795,0.0008688068,0.0003216216,0.0003014373,0.0005276235,0.000185535],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001691418,0.000006899716,0.00007787057,0.00003470125,0.000003772333,0.00005629797,0.0001688367,0.0005169813,0.0006636095,0.9891164,0.00232192,0.007015808],"study_design_scores_gemma":[0.000006978272,0.00000933146,0.0001328408,0.00001784651,0.000007858148,0.00009891576,0.00002600384,0.004158217,0.0003734276,0.9872928,0.007859404,0.0000164063],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1853863,0.01477909,0.5760031,0.006146549,0.005440957,0.0001700443,0.001062282,0.0009923434,0.2100193],"genre_scores_gemma":[0.7498611,0.006104658,0.1406367,0.002296623,0.003801143,0.0003359325,0.001025485,0.0008042188,0.09513415],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009488428,"threshold_uncertainty_score":0.03174198,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2937203737","doi":"10.3390/sym11040538","title":"A Note on the Truncated-Exponential Based Apostol-Type Polynomials","year":2019,"lang":"en","type":"article","venue":"Symmetry","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":33,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Difference polynomials; Classical orthogonal polynomials; Orthogonal polynomials; Discrete orthogonal polynomials; Wilson polynomials; Pure mathematics; Hahn polynomials; Macdonald polynomials; Type (biology); Hermite polynomials; Gegenbauer polynomials; Exponential polynomial; Exponential function; Mathematical analysis","authors":[{"name":"H. M. Srivastava","is_ca":true},{"name":"Serkan Aracı","is_ca":false},{"name":"Waseem Ahmad Khan","is_ca":false},{"name":"Mehmet Açıkgöz","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03939577885766999,"gpt":0.3194350639198177,"spread":0.2800392850621478,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006698786,0.0003020041,0.000307059,0.0006993742,0.000691909,0.0007074802,0.0005912551,0.0004569473,0.00373969],"category_scores_gemma":[0.001677768,0.0001097277,0.0004671804,0.0006352811,0.001634988,0.002319617,0.0009923172,0.001559415,0.0006824625],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005860815,"about_ca_system_score_gemma":0.0006622716,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006683771,"about_ca_topic_score_gemma":0.0005326046,"domain_scores_codex":[0.9997242,0.00006519507,0.000011311,0.00004080014,0.0001084821,0.00005001364],"domain_scores_gemma":[0.9995889,0.0001134701,0.00006171121,0.0000626336,0.0001167956,0.0000565533],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001074103,0.000007899706,0.0001164874,0.00002633218,0.000001426174,0.00008591499,0.00007105763,0.0009664823,0.001334268,0.9918073,0.0005716092,0.00500034],"study_design_scores_gemma":[0.000008205493,0.00004318343,0.0002518316,0.00001649382,0.000004335954,0.0003425773,0.00007254355,0.02011898,0.001400562,0.9677896,0.009934231,0.00001748943],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3250307,0.00434817,0.5049361,0.003402734,0.00107801,0.00006198257,0.0002769565,0.0001796062,0.1606858],"genre_scores_gemma":[0.9276649,0.00265639,0.04836227,0.0006070404,0.0008373084,0.0000290013,0.0001064584,0.00006912008,0.01966734],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00373969,"threshold_uncertainty_score":0.01251048,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1978706659","doi":"10.1016/j.jnt.2009.02.015","title":"Higher-order recurrences for Bernoulli numbers","year":2009,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":32,"is_retracted":false,"has_abstract":false,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada; University of Tokyo; Ministry of Education, Culture, Sports, Science and Technology","keywords":"Mathematics; Bernoulli number; Notation; Euler's formula; Bernoulli's principle; Order (exchange); Euler number (physics); Discrete mathematics; Pure mathematics; Type (biology); Arithmetic; Mathematical analysis; Euler equations; Backward Euler method; Semi-implicit Euler method","authors":[{"name":"Takashi Agoh","is_ca":false},{"name":"Karl Dilcher","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.05392408236078486,"gpt":0.3800742801057894,"spread":0.3261501977450045,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002809657,0.0008942049,0.001409325,0.00383808,0.002262199,0.004442313,0.001569973,0.001444138,0.007762527],"category_scores_gemma":[0.009409815,0.0006095472,0.001197722,0.002842508,0.003446477,0.005490399,0.001941341,0.003128516,0.002293496],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002619275,"about_ca_system_score_gemma":0.001166798,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001509213,"about_ca_topic_score_gemma":0.002541945,"domain_scores_codex":[0.998602,0.0003280371,0.0001289597,0.0001877442,0.0005028898,0.0002504478],"domain_scores_gemma":[0.9968538,0.001407077,0.0004677743,0.0004161647,0.0005813417,0.0002739376],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000016457,0.0000139917,0.0002401024,0.00003438899,0.000004942647,0.0001088482,0.0002545771,0.0005751945,0.0005657795,0.9921383,0.001219603,0.004827817],"study_design_scores_gemma":[0.000007029046,0.000006622387,0.0001561944,0.00001614812,0.000006186445,0.0001240039,0.00003146008,0.003899931,0.0002704065,0.992799,0.002666395,0.00001643889],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.3689906,0.01129887,0.3370662,0.005639461,0.004077451,0.0001448734,0.0006389326,0.0009081621,0.2712354],"genre_scores_gemma":[0.8964686,0.003510366,0.04470159,0.000985218,0.00206663,0.0001384123,0.0003745344,0.0003296711,0.05142501],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007762527,"threshold_uncertainty_score":0.02596819,"prediction_status":"machine_predicted_unvalidated"},"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,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"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","authors":[{"name":"Ayşe Alaca","is_ca":true},{"name":"Şaban Alaca","is_ca":true},{"name":"Mathieu F. Lemire","is_ca":true},{"name":"Kenneth S. Williams","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03479522734411008,"gpt":0.3442587681776741,"spread":0.3094635408335641,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001194933,0.0006543841,0.0005446756,0.003063387,0.001735314,0.002104546,0.0008751612,0.0009569843,0.007556219],"category_scores_gemma":[0.003889539,0.00027585,0.0006710373,0.002013271,0.002675893,0.003312778,0.001362071,0.001734464,0.001307509],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001066884,"about_ca_system_score_gemma":0.0004937116,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002393516,"about_ca_topic_score_gemma":0.0002122439,"domain_scores_codex":[0.9992085,0.0001737087,0.00005502413,0.0001232585,0.0002889061,0.0001506363],"domain_scores_gemma":[0.9986285,0.0004308875,0.000321,0.0001462095,0.0002544458,0.0002191024],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002847198,0.0000198716,0.0004386472,0.00003690033,0.000003380659,0.000117874,0.0002558461,0.0007400019,0.002494438,0.9867268,0.000776145,0.008361659],"study_design_scores_gemma":[0.00001510139,0.00005030624,0.0005365641,0.00002809031,0.00000903521,0.000466221,0.0001869548,0.007431209,0.002448293,0.9833156,0.005489153,0.0000235168],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6375178,0.001676578,0.2563779,0.001175151,0.000956775,0.0001282277,0.0003480976,0.0002565063,0.101563],"genre_scores_gemma":[0.9573101,0.0007608253,0.02656055,0.0002370615,0.000493749,0.00009644999,0.0001984533,0.00006816083,0.01427451],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007556219,"threshold_uncertainty_score":0.02527809,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null}]}