{"meta":{"page":1,"per_page":50,"max_per_page":100,"total":103,"total_is_capped":false,"direct_labels_cover":0,"predictions_cover":103,"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":"98144c5cd33c","filters":{"venue":"Bulletin of the Australian Mathematical Society"}},"results":[{"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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.003844331,0.0002259312,0.0005210441,0.00002465024,0.0001403978,0.00001834137,0.0004902985,0.0001355142,0.00110824],"category_scores_gemma":[0.002177957,0.0001374554,0.0005968577,0.0002441628,0.000861761,0.00005813253,0.0001947852,0.0002279251,0.00002488293],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001174621,"about_ca_system_score_gemma":0.00005797841,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002116602,"about_ca_topic_score_gemma":0.00002329046,"domain_scores_codex":[0.9964061,0.0003718579,0.001142697,0.0002075215,0.001579616,0.0002921681],"domain_scores_gemma":[0.9959973,0.001626671,0.0009748436,0.0007314836,0.0006326652,0.00003709018],"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":[0.00001576984,0.0006968222,0.0004620001,0.001914493,0.0002446907,6.613246e-8,0.001204111,0.0006770023,0.007713353,0.9480711,0.03890435,0.00009627992],"study_design_scores_gemma":[0.0006547262,0.0000409851,0.001170142,0.0004376177,0.0008506582,0.000003160528,0.001341,0.002114723,0.01573421,0.9772718,0.0002409004,0.0001400849],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9611591,0.0001857587,0.02266043,0.003518297,0.0002891604,0.00223515,0.00003818072,0.00008366982,0.009830264],"genre_scores_gemma":[0.9812088,0.000004665572,0.01306587,0.00002060642,0.00007116806,0.00004947748,0.00000297314,0.00003377005,0.005542682],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03866345,"threshold_uncertainty_score":0.9998049,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1984636682","doi":"10.1017/s0004972700034316","title":"Approximation by functions with bounded derivative on Banach spaces","year":2004,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Approximation Theory and Sequence Spaces","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"St. Francis Xavier University","funders":"","keywords":"Mathematics; Bounded function; Banach space; Separable space; Norm (philosophy); Derivative (finance); Pure mathematics; Uniform continuity; Bounded inverse theorem; Approximation property; Discrete mathematics; Bounded operator; Mathematical analysis","authors":[{"name":"R. Fry","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03104541416700255,"gpt":0.2722172759360887,"spread":0.2411718617690862,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005433314,0.0002562541,0.0003408563,0.00001735773,0.0003263552,0.00006294464,0.0003621026,0.0001528292,0.0008806143],"category_scores_gemma":[0.0003400781,0.0001527065,0.0002605413,0.0002395754,0.0006113865,0.0000582137,0.00005343612,0.000296166,0.0001283631],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001274079,"about_ca_system_score_gemma":0.00004838809,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001383804,"about_ca_topic_score_gemma":9.726898e-7,"domain_scores_codex":[0.9983862,0.0001067553,0.0004015928,0.0002685548,0.0005406044,0.0002963117],"domain_scores_gemma":[0.9985529,0.0003900197,0.0003683515,0.000501014,0.0001008609,0.00008683167],"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":[0.00006080475,0.0007555358,0.00004908605,0.0004930484,0.0002067411,4.944614e-7,0.00489897,0.0001736978,0.001574809,0.9055375,0.08619764,0.00005162873],"study_design_scores_gemma":[0.001052942,0.00024207,0.00007030743,0.0004768404,0.0001293106,0.00001646133,0.007831423,0.00004570016,0.04197139,0.9433051,0.004533062,0.000325405],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7702087,0.0000145638,0.1448409,0.05715936,0.0001144931,0.002119336,0.00009475696,0.000319811,0.02512804],"genre_scores_gemma":[0.8812963,0.000002638225,0.1030737,0.0004045178,0.00004708121,0.00009872387,0.00001082846,0.00004547098,0.01502063],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1110877,"threshold_uncertainty_score":0.9642109,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1974036436","doi":"10.1017/s0004972700020232","title":"Amenability and topological centres of the second duals of Banach algebras","year":2002,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Manitoba","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Dual polyhedron; Banach algebra; Dual (grammatical number); Pure mathematics; Locally compact group; Product (mathematics); Algebra over a field; Locally compact space; Banach space","authors":[{"name":"F. Ghahramani","is_ca":true},{"name":"Javad Laali","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.0575584063700818,"gpt":0.3114586871058674,"spread":0.2539002807357856,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008372923,0.0001979451,0.0005606317,0.00001020458,0.0001123024,0.00001266282,0.0006869111,0.0001811029,0.01197893],"category_scores_gemma":[0.001726168,0.0001044894,0.0004611118,0.0001887028,0.001697683,0.00002231931,0.0004990179,0.0003560015,0.00001320217],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004083657,"about_ca_system_score_gemma":0.00001597581,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009604801,"about_ca_topic_score_gemma":0.000002624163,"domain_scores_codex":[0.9977602,0.0002876962,0.000743873,0.0002568406,0.0006076628,0.000343727],"domain_scores_gemma":[0.9972683,0.001295829,0.0003367377,0.0008685532,0.0001364896,0.00009411765],"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":[0.0000424033,0.002549442,0.01383989,0.007155629,0.00051217,0.000001362769,0.007259841,0.0000113613,0.01219165,0.7350362,0.2209982,0.0004018641],"study_design_scores_gemma":[0.001149569,0.0001847913,0.009216086,0.0004218968,0.000155333,0.00002504269,0.003294707,0.0001960862,0.1408021,0.8372397,0.006956258,0.000358333],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9895107,0.00004963184,0.00005488396,0.008112245,0.00003617803,0.0006313077,0.00004177756,0.00001619055,0.001547159],"genre_scores_gemma":[0.9737387,0.00001150848,0.01576268,0.000100872,0.00002148441,0.00001380124,2.21296e-7,0.00001960143,0.01033116],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2140419,"threshold_uncertainty_score":0.9889243,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W3093467580","doi":"10.1017/s0004972721000095","title":"FUSION 2-CATEGORIES WITH NO LINE OPERATORS ARE GROUPLIKE","year":2021,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Homotopy and Cohomology in Algebraic Topology","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Perimeter Institute; Dalhousie University","funders":"","keywords":"Indecomposable module; Endomorphism; Real line; Object (grammar); Fusion; Line (geometry)","authors":[],"retraction":null,"screen_n_in":null,"score":{"opus":0.02776866379419688,"gpt":0.2762295929004122,"spread":0.2484609291062153,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0004447984,0.0002585405,0.0005493305,0.000009446621,0.0002221614,0.0000278282,0.0004650313,0.0002997592,0.007259978],"category_scores_gemma":[0.0006673224,0.0001559759,0.0003625759,0.0001965226,0.0007281965,0.00001939121,0.0002839639,0.0004243765,0.0002702042],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003641467,"about_ca_system_score_gemma":0.00007089583,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008460934,"about_ca_topic_score_gemma":0.000004489704,"domain_scores_codex":[0.9982632,0.0001713789,0.0005013125,0.0003219565,0.0003559534,0.0003861671],"domain_scores_gemma":[0.9981093,0.0005094195,0.0002700376,0.0007641787,0.0002448843,0.0001022161],"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":[0.000077746,0.001538733,0.002541687,0.001825447,0.0006480301,0.00006402354,0.002977377,0.00001157264,0.003032688,0.7264096,0.2607291,0.0001440301],"study_design_scores_gemma":[0.002278854,0.0004233888,0.001741257,0.0009391508,0.000630462,0.0006798478,0.0074466,0.00008467771,0.07846408,0.832913,0.07343488,0.000963775],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9348801,0.00005714822,0.002638912,0.05234275,0.0004108124,0.0006687954,0.00003253458,0.0001737041,0.008795266],"genre_scores_gemma":[0.8345175,0.00002605829,0.08310023,0.001559849,0.0002636931,0.00006976687,0.00000758363,0.00007763852,0.08037763],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1872942,"threshold_uncertainty_score":0.9936475,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2126790654","doi":"10.1017/s0004972700020268","title":"Weakly compact sets and smooth norms in Banach spaces","year":2002,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Banach Space Theory","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Alberta","funders":"Grantová Agentura České Republiky","keywords":"Mathematics; Banach space; Pointwise; Pure mathematics; Smoothness; Eberlein–Šmulian theorem; Lp space; Mathematical analysis","authors":[{"name":"Marián Fabian","is_ca":false},{"name":"Vicente Montesinos","is_ca":false},{"name":"Václav Zizler","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04411497676948656,"gpt":0.2967271179496684,"spread":0.2526121411801818,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007367571,0.0002935914,0.0005772492,0.00002722172,0.0001058439,0.00003457019,0.0004617882,0.0001802286,0.002561613],"category_scores_gemma":[0.0005641413,0.0001950793,0.0002991535,0.0002073979,0.0005708223,0.00004331516,0.0001610954,0.0004254322,0.0001078445],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008209468,"about_ca_system_score_gemma":0.000008115298,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003039838,"about_ca_topic_score_gemma":0.000006431173,"domain_scores_codex":[0.9981443,0.0001360377,0.0005308991,0.0002925667,0.0004212022,0.0004749986],"domain_scores_gemma":[0.9980683,0.0008603072,0.0002735427,0.0006305998,0.0000378096,0.0001294519],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00004581321,0.00195113,0.00548639,0.003378899,0.0003132035,0.00001263273,0.01383757,0.0001116957,0.002405351,0.2960913,0.6753744,0.0009916718],"study_design_scores_gemma":[0.001720674,0.0001290063,0.005831684,0.0009986199,0.0001703404,0.00005872898,0.004930863,0.001400378,0.003132968,0.9584147,0.02242607,0.0007859905],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.943252,0.0001349831,0.0006035755,0.04219182,0.00008614935,0.001049005,0.00003288157,0.000140136,0.01250949],"genre_scores_gemma":[0.9485839,0.0000340947,0.03573699,0.0002447572,0.00003747521,0.0000124378,7.27774e-7,0.00005544696,0.01529417],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6623234,"threshold_uncertainty_score":0.9983502,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2109887555","doi":"10.1017/s0004972714000197","title":"THE MINIMAL GROWTH OF A -REGULAR SEQUENCE","year":2014,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"semigroups and automata theory","field":"Computer Science","cited_by":20,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Multiplicative function; Sequence (biology); Combinatorics; Constant (computer programming); Discrete mathematics; Mathematical analysis","authors":[{"name":"Jason P. Bell","is_ca":true},{"name":"Michael James Coons","is_ca":false},{"name":"Kevin G. Hare","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.01835345285741214,"gpt":0.2389289914033845,"spread":0.2205755385459724,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001359721,0.0001351692,0.000234268,0.000006103725,0.0001708766,0.00005335881,0.002131975,0.00007974518,0.00008872039],"category_scores_gemma":[0.000344072,0.00007036151,0.0003940605,0.0001674763,0.0006078972,0.00003115106,0.000435973,0.0001472009,0.0000518325],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001615322,"about_ca_system_score_gemma":0.00001940608,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001388609,"about_ca_topic_score_gemma":1.220473e-7,"domain_scores_codex":[0.9985448,0.0001539234,0.0003997548,0.0002011222,0.0004196642,0.0002807816],"domain_scores_gemma":[0.9979848,0.0007230524,0.0002513372,0.0008995314,0.00007987423,0.0000613864],"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":[0.000002714788,0.00007587012,0.00006864926,0.0001578134,0.00004056043,2.02074e-7,0.0006024233,0.000004511645,0.004130641,0.9462682,0.0475443,0.001104098],"study_design_scores_gemma":[0.0005695926,0.0001599373,0.002705225,0.0003889482,0.00006025068,0.00004221017,0.0004592869,0.01326557,0.07727116,0.8633232,0.04137307,0.0003815789],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4552406,0.0001557488,0.3130325,0.2164484,0.0008112327,0.001499798,0.00003128478,0.0004375339,0.0123428],"genre_scores_gemma":[0.9248968,0.000005616864,0.07172911,0.0003978683,0.00004681039,0.0000112058,2.556554e-7,0.00001119879,0.00290117],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4696561,"threshold_uncertainty_score":0.3961775,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2073800962","doi":"10.1017/s0004972700037709","title":"Connes-amenability and normal, virtual diagonals for measure algebras, II","year":2003,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Diagonal; Locally compact group; Locally compact space; Measure (data warehouse); Pure mathematics; Algebra over a field; Geometry; Computer science; Data mining","authors":[{"name":"Volker Runde","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.05600345711199827,"gpt":0.3283682768606991,"spread":0.2723648197487008,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002326594,0.0002903436,0.0005592835,0.00001381169,0.0004141442,0.00004114762,0.0004589256,0.0002199207,0.001647046],"category_scores_gemma":[0.005960783,0.0001968989,0.0004840143,0.0001521864,0.0007206122,0.00004462831,0.0002374595,0.0003487586,0.0000221766],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007620485,"about_ca_system_score_gemma":0.00007483548,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002984649,"about_ca_topic_score_gemma":9.345594e-7,"domain_scores_codex":[0.9975538,0.00024175,0.0006410195,0.0003960472,0.0006119098,0.0005554881],"domain_scores_gemma":[0.9967191,0.001907169,0.0002019983,0.0007253609,0.0002490529,0.0001973637],"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":[0.00004120698,0.0006893169,0.000369878,0.001229202,0.0002394563,5.180858e-7,0.001509407,0.000007023813,0.002155823,0.867072,0.1261957,0.0004904311],"study_design_scores_gemma":[0.001808599,0.000323181,0.000261134,0.0002505605,0.0001645697,0.00002999795,0.002042881,0.00007011168,0.03650058,0.9147187,0.04333773,0.0004919312],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9673742,0.0001023985,0.01240277,0.01501913,0.000131335,0.00307206,0.0001196677,0.0001096677,0.001668791],"genre_scores_gemma":[0.8759848,0.00001318268,0.1131622,0.0003409362,0.0000667799,0.0002281029,0.000002094946,0.0000745023,0.01012729],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1007595,"threshold_uncertainty_score":0.9992656,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2157960833","doi":"10.1017/s0004972700018700","title":"A note on <i>p</i>-adic Carlitz's <i>q</i>-Bernoulli numbers","year":2000,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":15,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Simon Fraser University","funders":"","keywords":"Mathematics; Bernoulli number; Bernoulli's principle; Generating function; Invariant (physics); Combinatorics; Function (biology); Bernoulli polynomials; Measure (data warehouse); Discrete mathematics; Pure mathematics; Orthogonal polynomials; Mathematical physics; Difference polynomials","authors":[{"name":"Taekyun Kim","is_ca":true},{"name":"Seog-Hoon Rim","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03110060763784918,"gpt":0.3030944594526701,"spread":0.2719938518148209,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0007063837,0.0004664971,0.0007800457,0.00002069172,0.000250678,0.00006447202,0.001014688,0.0002910537,0.01667795],"category_scores_gemma":[0.0007990101,0.0003216027,0.001100016,0.000263438,0.0008130029,0.00005250005,0.000163611,0.0006052183,0.001696049],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001372604,"about_ca_system_score_gemma":0.00003957243,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002846098,"about_ca_topic_score_gemma":0.000001492997,"domain_scores_codex":[0.9966478,0.0001550019,0.000987718,0.0004589984,0.001041521,0.0007090022],"domain_scores_gemma":[0.9965758,0.001459405,0.0003215127,0.001334843,0.00009040795,0.000218018],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00006957873,0.00152175,0.00004277564,0.002512288,0.0002946278,0.000007749207,0.004129736,0.000125213,0.0006244291,0.3581854,0.6316322,0.000854196],"study_design_scores_gemma":[0.0006879415,0.00008301161,0.00004473512,0.0006969943,0.0001969063,0.00003569957,0.000515368,0.0000831654,0.005061157,0.9073458,0.08481193,0.0004372753],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"other","genre_scores_codex":[0.4762478,0.00008207112,0.005993959,0.05449551,0.0006848422,0.004577745,0.0002388866,0.001207154,0.456472],"genre_scores_gemma":[0.3274515,0.00006255631,0.1760441,0.002295904,0.0003698439,0.0001869945,0.000005817888,0.0002852766,0.493298],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.5491604,"threshold_uncertainty_score":0.9999236,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2047209794","doi":"10.1017/s0004972710000390","title":"ENDPOINT ESTIMATES FOR COMMUTATORS OF RIESZ TRANSFORMS ASSOCIATED WITH SCHRÖDINGER OPERATORS","year":2010,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Harmonic Analysis Research","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"","funders":"Memorial University of Newfoundland","keywords":"Mathematics; Commutator; Riesz transform; Bounded function; Hardy space; Operator (biology); Combinatorics; Space (punctuation); Pure mathematics; Mathematical analysis; Algebra over a field","authors":[{"name":"Pengtao Li","is_ca":false},{"name":"Lizhong Peng","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04556186344676916,"gpt":0.3379079310241035,"spread":0.2923460675773344,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001323699,0.0002689425,0.0007260813,0.00002675176,0.0002046372,0.00002910577,0.0007226605,0.0002215668,0.001752452],"category_scores_gemma":[0.002370365,0.0001545243,0.0006759808,0.0002761726,0.00100673,0.00003893351,0.0001088252,0.0005610707,0.00001104913],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005327216,"about_ca_system_score_gemma":0.00007844034,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001015522,"about_ca_topic_score_gemma":0.000007653303,"domain_scores_codex":[0.9978364,0.00005914087,0.0007322406,0.000245591,0.0006566447,0.0004700525],"domain_scores_gemma":[0.9965629,0.001926952,0.0003981639,0.000649659,0.0003356074,0.0001267227],"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":[0.0003681587,0.004260099,0.005143335,0.005101113,0.005344707,0.000003240514,0.01037776,0.0002357586,0.05338532,0.8385376,0.0764097,0.0008331725],"study_design_scores_gemma":[0.003154845,0.0003793066,0.001159227,0.0009013658,0.001150576,0.00001460373,0.003747003,0.002532081,0.2602221,0.7207084,0.005256647,0.0007738144],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9193425,0.0000166212,0.06757096,0.009035598,0.00008142903,0.002284713,0.00022992,0.0001023719,0.001335863],"genre_scores_gemma":[0.8452185,0.000001980494,0.1525234,0.0000347618,0.00001932893,0.00007460632,0.000006525569,0.00005579881,0.00206504],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2068368,"threshold_uncertainty_score":0.9991601,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2010382593","doi":"10.1017/s0004972700038508","title":"Permutation representations and rational irreducibility","year":2005,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Transitive relation; Combinatorics; Primitive permutation group; Simple (philosophy); Irreducibility; Affine transformation; Group (periodic table); Character (mathematics); Permutation group; Simple group; Discrete mathematics; Permutation (music); Symmetric group; Pure mathematics; Cyclic permutation","authors":[],"retraction":null,"screen_n_in":null,"score":{"opus":0.08305924284248177,"gpt":0.3660392491240794,"spread":0.2829800062815976,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001338651,0.0001318936,0.0002155078,0.00001479552,0.0001838932,0.00003907325,0.000285319,0.0001025163,0.003052998],"category_scores_gemma":[0.001750251,0.00009341969,0.0002380287,0.0001326696,0.000523219,0.00004390952,0.0001651228,0.000236737,0.0001017609],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005704227,"about_ca_system_score_gemma":0.00003296835,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007287982,"about_ca_topic_score_gemma":0.000001229059,"domain_scores_codex":[0.9983853,0.0001868292,0.0004610986,0.0002579479,0.0004813081,0.0002274932],"domain_scores_gemma":[0.9978412,0.001254641,0.0001522365,0.0005459538,0.000121103,0.00008479693],"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":[0.00002984466,0.0007057509,0.001276775,0.0007133332,0.0001418794,3.640776e-7,0.005374725,0.00005109364,0.003217187,0.7680719,0.2194867,0.0009304051],"study_design_scores_gemma":[0.0006519373,0.00003809455,0.007352104,0.0001069718,0.00008824874,0.00003307802,0.001706515,0.00118688,0.006791279,0.9727761,0.00905079,0.0002179629],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9250464,0.00001733265,0.002663628,0.06330512,0.00005005025,0.0009339982,0.00004360494,0.0000809346,0.007858939],"genre_scores_gemma":[0.8938022,0.000003468459,0.08870076,0.0001650662,0.0001078638,0.00004131954,0.000004205755,0.00002269081,0.01715244],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2104359,"threshold_uncertainty_score":0.9978583,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2080845342","doi":"10.1017/s0004972709000616","title":"COMBINATORIAL REES–SUSHKEVICH VARIETIES THAT ARE CROSS, FINITELY GENERATED, OR SMALL","year":2009,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"semigroups and automata theory","field":"Computer Science","cited_by":12,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Simon Fraser University","funders":"","keywords":"Subvariety; Mathematics; Variety (cybernetics); Combinatorics; Finitely-generated abelian group; Set (abstract data type); Generating set of a group; Lattice (music); Discrete mathematics; Pure mathematics; Computer science; Geometry","authors":[{"name":"Edmond W. H. Lee","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04588173806011037,"gpt":0.2660268186568844,"spread":0.220145080596774,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008608514,0.0002874751,0.0004358969,0.00001539811,0.0002858551,0.0003142011,0.002087829,0.0002478152,0.000638208],"category_scores_gemma":[0.0002415553,0.0001757104,0.0004671765,0.0002872688,0.0003126691,0.00007191129,0.0003888682,0.0003450624,0.0001427335],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004630283,"about_ca_system_score_gemma":0.00005656008,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001319366,"about_ca_topic_score_gemma":3.799211e-7,"domain_scores_codex":[0.9979466,0.000149938,0.0004897981,0.0004055524,0.000527373,0.0004807898],"domain_scores_gemma":[0.9979661,0.0003606996,0.0003431114,0.001081439,0.0001176676,0.0001309972],"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":[0.0000504549,0.0007238528,0.000501634,0.0002991601,0.0001196432,0.00001367012,0.001680093,0.00008293633,0.0006822111,0.7723262,0.2225105,0.001009593],"study_design_scores_gemma":[0.00234717,0.0004081987,0.01258367,0.0005552957,0.0001012142,0.0001151719,0.0006464975,0.003884332,0.02656295,0.8762961,0.07545524,0.001044173],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6781291,0.0003910585,0.124707,0.1706159,0.004620677,0.002956619,0.0001099462,0.001978983,0.01649072],"genre_scores_gemma":[0.9185855,0.00002042714,0.06390397,0.002831254,0.0002701476,0.00001865809,0.000003052092,0.00002930884,0.01433768],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2404564,"threshold_uncertainty_score":0.7165263,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2171158068","doi":"10.1017/s0004972700018694","title":"Maximal ideals and the structure of contractible and amenable Banach algebras","year":2000,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Contractible space; Ideal (ethics); Banach algebra; Pure mathematics; Subspace topology; Maximal ideal; Banach space; Discrete mathematics; Mathematical analysis","authors":[{"name":"Yong Zhang","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02228896052374671,"gpt":0.2966308859358309,"spread":0.2743419254120842,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008213954,0.0002133958,0.0005728464,0.00001090518,0.000189465,0.00004600873,0.0004226449,0.0001539725,0.005295464],"category_scores_gemma":[0.0005815702,0.0001123451,0.0002175281,0.0001429002,0.001446146,0.00003992669,0.0001743365,0.000404787,0.00001289382],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002376967,"about_ca_system_score_gemma":0.00002766662,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004387166,"about_ca_topic_score_gemma":0.000001845103,"domain_scores_codex":[0.9981493,0.0001972109,0.0005435699,0.0002412887,0.0005048339,0.0003637643],"domain_scores_gemma":[0.9976534,0.001406157,0.0001971598,0.0005530166,0.00008721971,0.0001030358],"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":[0.0004131996,0.0004181079,0.0006660409,0.00314441,0.0007192441,0.000002902864,0.005282542,0.00004790241,0.01256367,0.8899803,0.08482176,0.001939941],"study_design_scores_gemma":[0.00266298,0.00007948765,0.0007014519,0.0002386414,0.0001902443,0.00006970933,0.001446501,0.0002835127,0.0234383,0.965169,0.005471248,0.000248922],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9854716,0.0001209462,0.0001625976,0.01163316,0.00001764087,0.0009265185,0.00004519009,0.00002496809,0.001597355],"genre_scores_gemma":[0.9615606,0.00007128985,0.02934592,0.0002233877,0.00003715578,0.00001098362,7.632749e-7,0.00003419117,0.008715691],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07935051,"threshold_uncertainty_score":0.9956138,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2043084809","doi":"10.1017/s0004972711002322","title":"ON A PROBLEM ON NORMAL NUMBERS RAISED BY IGOR SHPARLINSKI","year":2011,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Université Laval","funders":"","keywords":"Mathematics; Irrational number; Combinatorics; Integer (computer science); Sequence (biology); Prime number; Limiting; Prime factor; Prime (order theory); Rational number; Discrete mathematics; Geometry","authors":[{"name":"Jean–Marie De Koninck","is_ca":true},{"name":"Imre Kátai","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.06607353085514854,"gpt":0.3097669891159802,"spread":0.2436934582608316,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001515054,0.0003630461,0.0005571576,0.00002295459,0.0001918913,0.0000324696,0.001097821,0.0002605725,0.01781787],"category_scores_gemma":[0.0007367792,0.0002361154,0.0007823394,0.0002120224,0.000636618,0.00002482941,0.0002328375,0.0006661274,0.001442641],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000108022,"about_ca_system_score_gemma":0.00005077891,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002972231,"about_ca_topic_score_gemma":6.20493e-7,"domain_scores_codex":[0.9969276,0.000250218,0.0007194045,0.000407183,0.001013416,0.0006822353],"domain_scores_gemma":[0.9971022,0.001198826,0.0003234836,0.00103684,0.0001009994,0.0002376408],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001146037,0.001225648,0.00008248157,0.0004271817,0.0002164423,0.000002135235,0.002006211,0.000001738455,0.0002464177,0.3028559,0.6927713,0.00004994066],"study_design_scores_gemma":[0.001638547,0.0004083479,0.00008627325,0.0006409647,0.000161772,0.00001869125,0.001467876,0.00009671209,0.01541273,0.9627089,0.01682272,0.0005364952],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.4029612,0.00001006602,0.003595475,0.0210886,0.0002224546,0.003836835,0.0002130824,0.0004232692,0.567649],"genre_scores_gemma":[0.7575561,0.000004960812,0.05591905,0.001033322,0.000103864,0.0001443027,0.00000638362,0.0001680907,0.1850639],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6759486,"threshold_uncertainty_score":0.9993349,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W64021027","doi":"10.1017/s0004972711002115","title":"INDECOMPOSABLE REPRESENTATIONS OF THE EUCLIDEAN ALGEBRA 𝔢(3) FROM IRREDUCIBLE REPRESENTATIONS OF","year":2011,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Toronto","funders":"University of Toronto","keywords":"Indecomposable module; Mathematics; Complexification; Eight-dimensional space; (g,K)-module; Lie algebra; Pure mathematics; Algebra over a field; Euclidean geometry; Euclidean group; Euclidean space; Lie conformal algebra; Combinatorics; Euclidean distance matrix; Seven-dimensional space; Adjoint representation of a Lie algebra; Geometry","authors":[{"name":"Andrew Douglas","is_ca":false},{"name":"Joe Repka","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.08808096219943903,"gpt":0.3387942149795835,"spread":0.2507132527801444,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005314079,0.0002139252,0.0005143136,0.00002184359,0.0001498642,0.00001091984,0.001199484,0.0001728942,0.00416727],"category_scores_gemma":[0.001565512,0.0001391924,0.0007508674,0.0003580879,0.0008785297,0.00004723061,0.0005100823,0.0003510099,0.00003127732],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003817701,"about_ca_system_score_gemma":0.00005617968,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002308609,"about_ca_topic_score_gemma":0.000005291462,"domain_scores_codex":[0.9974787,0.0001946626,0.00112327,0.0003173409,0.0006031767,0.0002828045],"domain_scores_gemma":[0.9956958,0.001197048,0.0009663567,0.001867696,0.0001968019,0.00007627845],"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":[0.00002107501,0.001184542,0.006111258,0.0006155004,0.0004957989,5.168626e-7,0.0115179,0.00002412987,0.007418646,0.8701781,0.1023553,0.00007718853],"study_design_scores_gemma":[0.0003466152,0.00002092602,0.006216261,0.0002470397,0.0001855829,0.000003689766,0.002368797,0.00002505398,0.1283659,0.8615634,0.0005286891,0.0001281295],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9560928,0.00003584179,0.005989337,0.007077906,0.0004097465,0.00153053,0.0002286219,0.00008413903,0.02855105],"genre_scores_gemma":[0.7321252,0.000008251865,0.257074,0.0000864216,0.00005678413,0.00003654684,0.000003911281,0.00004615227,0.01056279],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2510846,"threshold_uncertainty_score":0.9967431,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2149963403","doi":"10.1017/s0004972713000208","title":"ON PERMUTATION BINOMIALS OVER FINITE FIELDS","year":2013,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":9,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Brock University","funders":"","keywords":"Finite field; Binomial (polynomial); Gaussian binomial coefficient; Permutation (music); Partial permutation; Binomial coefficient; Cyclic permutation; Generalized permutation matrix; Divisor (algebraic geometry)","authors":[],"retraction":null,"screen_n_in":null,"score":{"opus":0.01706719996674736,"gpt":0.2392756072454778,"spread":0.2222084072787304,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0003273868,0.0001138845,0.0001516797,0.00001371385,0.0001094903,0.00008372807,0.0007549356,0.00009605086,0.002830412],"category_scores_gemma":[0.0001485936,0.00007356977,0.0003706184,0.0001551841,0.0001195975,0.00004353826,0.0001587299,0.0001578479,0.0004793336],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001278741,"about_ca_system_score_gemma":0.000009527165,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001199367,"about_ca_topic_score_gemma":6.95813e-8,"domain_scores_codex":[0.9990605,0.00008207448,0.0002400321,0.0001804644,0.000245678,0.000191233],"domain_scores_gemma":[0.9986982,0.0005650494,0.0001119154,0.0005290126,0.00003915816,0.00005668623],"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":[0.000003325761,0.0001665793,0.00008648125,0.00008980232,0.00004525082,2.590333e-7,0.00127047,0.000159324,0.0005401847,0.7588515,0.2375595,0.001227347],"study_design_scores_gemma":[0.0003394015,0.0001130784,0.004058458,0.0001406049,0.00001999061,0.000003248559,0.000106905,0.003164422,0.004202613,0.9802467,0.007385202,0.0002194248],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.730898,0.00001120777,0.1863151,0.06627392,0.0004446562,0.0009961162,0.000007653607,0.0002413648,0.01481196],"genre_scores_gemma":[0.9788135,0.000001276069,0.01622331,0.001473125,0.00003134148,0.00002307857,3.719235e-7,0.000006543748,0.003427439],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2479155,"threshold_uncertainty_score":0.9980811,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2930774002","doi":"10.1017/s0004972719000352","title":"A BOUND FOR THE CHROMATIC NUMBER OF (, GEM)-FREE GRAPHS","year":2019,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":9,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Waterloo; Wilfrid Laurier University","funders":"","keywords":"Combinatorics; Unicode; Mathematics; Clique number; Vertex (graph theory); Graph; Chromatic scale; Discrete mathematics; Computer science","authors":[{"name":"Kathie Cameron","is_ca":true},{"name":"Shenwei Huang","is_ca":false},{"name":"Owen Merkel","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02564806360005934,"gpt":0.301924739568164,"spread":0.2762766759681046,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001238262,0.0001660847,0.0003337972,0.00001265536,0.0001491942,0.00005635104,0.003398762,0.00009440128,0.0008054753],"category_scores_gemma":[0.000414097,0.00009062185,0.0007108002,0.0003378883,0.0005892512,0.00005666723,0.0007596237,0.0002195587,0.0001590342],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002583935,"about_ca_system_score_gemma":0.00003892274,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009039252,"about_ca_topic_score_gemma":2.504476e-7,"domain_scores_codex":[0.9981908,0.00009874791,0.0004435402,0.0002641611,0.0006059178,0.000396798],"domain_scores_gemma":[0.9959269,0.001677449,0.0002541333,0.001930679,0.000144982,0.00006586852],"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":[0.00001404318,0.0001878853,0.000443378,0.001046084,0.000166385,1.749036e-7,0.001091849,0.00004747539,0.001601987,0.9369625,0.05815075,0.0002875048],"study_design_scores_gemma":[0.0007099226,0.00006756345,0.0008999388,0.0001520322,0.00003999459,0.00001542601,0.0003197046,0.002489929,0.005104966,0.9824685,0.007573503,0.000158509],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5646335,0.0001610847,0.3156545,0.09958696,0.00082181,0.008144777,0.0001061021,0.0002620598,0.01062908],"genre_scores_gemma":[0.7625541,0.000009457596,0.2179725,0.0004603119,0.00003855758,0.0001384976,7.601116e-7,0.00003805053,0.01878778],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1979205,"threshold_uncertainty_score":0.8819391,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2071351111","doi":"10.1017/s0004972709000148","title":"CONVOLUTIONS OF GENERIC ORBITAL MEASURES IN COMPACT SYMMETRIC SPACES","year":2009,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada; University of Waterloo; Sultan Qaboos University","keywords":"Mathematics; Haar measure; Measure (data warehouse); Absolute continuity; Symmetric space; Invariant (physics); Coset; Locally compact space; Combinatorics; Pure mathematics; Product (mathematics); Mathematical analysis; Geometry; Mathematical physics","authors":[{"name":"Sanjiv Kumar Gupta","is_ca":false},{"name":"Kathryn E. Hare","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.05439368871874302,"gpt":0.3069203191971193,"spread":0.2525266304783763,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005558007,0.0001966104,0.0005510586,0.00005974851,0.00006579651,0.00001283095,0.0004328936,0.0001384345,0.0004314876],"category_scores_gemma":[0.000984918,0.0001336397,0.0004785359,0.0007416506,0.0002851786,0.00002573154,0.0000555067,0.0002574381,0.00002719132],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005893771,"about_ca_system_score_gemma":0.0000281816,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000117101,"about_ca_topic_score_gemma":9.064171e-7,"domain_scores_codex":[0.9982756,0.00007300869,0.0006691439,0.0001849895,0.0004668069,0.0003304255],"domain_scores_gemma":[0.9984644,0.0005729814,0.0003422031,0.0004568989,0.00008436301,0.00007916122],"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":[0.00003691711,0.00248316,0.004073622,0.001092429,0.0002303554,0.000003740176,0.001790257,0.0003200112,0.005837313,0.8591653,0.1243269,0.0006400264],"study_design_scores_gemma":[0.0009210321,0.0001575606,0.02131462,0.0004492206,0.0001367252,0.00002745007,0.001263419,0.000169088,0.01321418,0.9603894,0.001609743,0.0003475024],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9858985,0.0001248034,0.002486212,0.007575299,0.00006134265,0.0004603157,0.00002478224,0.00004734034,0.003321412],"genre_scores_gemma":[0.9774466,0.000008771522,0.02082284,0.00007870165,0.00003022735,0.000003203827,7.483429e-7,0.00001406321,0.0015949],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1227171,"threshold_uncertainty_score":0.5449666,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2963880843","doi":"10.1017/s0004972708001172","title":"SKEW-PRODUCT DYNAMICAL SYSTEMS, ELLIS GROUPS AND TOPOLOGICAL CENTRE","year":2009,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":8,"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":"Skew; Mathematics; Ergodic theory; Dynamical systems theory; Type (biology); Product (mathematics); Pure mathematics; Dynamical system (definition); Topology (electrical circuits); Topological dynamics; Combinatorics; Computer science; Geometry; Functional analysis; Physics","authors":[{"name":"Ali Jabbari","is_ca":false},{"name":"Hamid Reza Ebrahimi Vishki","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03011771948242253,"gpt":0.277609812293755,"spread":0.2474920928113324,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0009470611,0.0003579021,0.0007799782,0.00001679125,0.000179521,0.00008766299,0.0005760113,0.0002804314,0.001106641],"category_scores_gemma":[0.001029927,0.0002186321,0.0005064995,0.0001510337,0.0004929949,0.00002938633,0.0002052682,0.0004544663,0.00007146603],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005601111,"about_ca_system_score_gemma":0.00001564464,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001017077,"about_ca_topic_score_gemma":4.100075e-7,"domain_scores_codex":[0.997374,0.0001657842,0.0008895117,0.0004378267,0.0005890766,0.000543832],"domain_scores_gemma":[0.9977556,0.0008052674,0.0003293437,0.000789864,0.00009592761,0.0002239426],"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":[0.0000101304,0.0005594234,0.00009326761,0.0007201119,0.00007372487,0.000002501502,0.0003713197,0.000003254506,0.0003432202,0.9440776,0.05357042,0.0001750598],"study_design_scores_gemma":[0.0004650257,0.00009774612,0.001126551,0.0004138632,0.0001901139,0.00008064678,0.0006170521,0.00324141,0.0002381338,0.9861938,0.006918607,0.0004170896],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8565211,0.0002410346,0.01843358,0.101562,0.0004204066,0.003011692,0.000147738,0.0004088748,0.01925358],"genre_scores_gemma":[0.9365333,0.00002700182,0.05142527,0.000365272,0.0001415765,0.00001177301,0.000003972752,0.00003538629,0.01145642],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1011967,"threshold_uncertainty_score":0.9998065,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2059098648","doi":"10.1017/s0004972712000421","title":"A NOTE CONCERNING THE DISTANCES OF UNIFORMLY DISTRIBUTED POINTS FROM THE CENTRE OF A RECTANGLE","year":2012,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Bayesian Methods and Mixture Models","field":"Computer Science","cited_by":8,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Alberta","funders":"","keywords":"Rectangle; Mathematics; Probability density function; Expression (computer science); Combinatorics; Function (biology); Cumulative distribution function; Closed-form expression; Geometry; Mathematical analysis; Statistics; Computer science","authors":[{"name":"Robert Stewart","is_ca":true},{"name":"Hong Zhang","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02828450385933519,"gpt":0.2666966735804778,"spread":0.2384121697211426,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001264899,0.000149402,0.0003204236,0.000003540988,0.0001276078,0.00002590665,0.00148318,0.00009266711,0.0001827021],"category_scores_gemma":[0.0003095013,0.00006601413,0.0004097426,0.0002129007,0.0004756398,0.0000463524,0.0003510993,0.0002286272,0.000008778115],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002503053,"about_ca_system_score_gemma":0.00002968386,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000823223,"about_ca_topic_score_gemma":0.000001610183,"domain_scores_codex":[0.9983709,0.0003025368,0.0004631686,0.0001559946,0.00040311,0.0003042884],"domain_scores_gemma":[0.9974337,0.00115836,0.0004512082,0.0008111456,0.00008002578,0.00006560802],"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":[0.00003885607,0.0006306815,0.003067738,0.0004593421,0.0004229125,5.644487e-7,0.04044133,0.00002329676,0.004922919,0.7822879,0.1608342,0.006870237],"study_design_scores_gemma":[0.002142607,0.000163243,0.02696856,0.002406739,0.000626247,0.0000270773,0.005921741,0.007826393,0.1058955,0.6965294,0.1504966,0.000995834],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02473969,0.0001632725,0.9317457,0.04193191,0.0001587336,0.0003793057,0.0001449192,0.00002454076,0.0007119358],"genre_scores_gemma":[0.7336186,0.000008871615,0.2655389,0.0002599114,0.00006115,0.000005283041,0.000002240502,0.000008999725,0.0004960938],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.7088789,"threshold_uncertainty_score":0.2756143,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2142435614","doi":"10.1017/s0004972711002334","title":"THE GENERALIZED SYLVESTER MATRIX EQUATION, RANK MINIMIZATION AND ROTH’S EQUIVALENCE THEOREM","year":2011,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Optimization Algorithms Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Regina","funders":"","keywords":"Mathematics; Sylvester equation; Sylvester matrix; Equivalence (formal languages); Sylvester's law of inertia; Rank (graph theory); Pure mathematics; Applied mathematics; Combinatorics; Algebra over a field; Mathematical analysis; Symmetric matrix; Eigenvalues and eigenvectors; Matrix polynomial","authors":[{"name":"Minghua Lin","is_ca":true},{"name":"Hȧrald K. Wimmer","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.09082908140697524,"gpt":0.3383889755654172,"spread":0.247559894158442,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001255651,0.0002295001,0.0003092275,0.0000175703,0.000407952,0.00007290054,0.0006637956,0.0001547176,0.001690411],"category_scores_gemma":[0.001309218,0.0001300927,0.0002584079,0.000219253,0.0008316134,0.00005993966,0.0003018193,0.0002523985,0.00005186006],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004895082,"about_ca_system_score_gemma":0.00003626874,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008266658,"about_ca_topic_score_gemma":4.825457e-7,"domain_scores_codex":[0.9977189,0.0002931964,0.0006803611,0.0002778481,0.0006238966,0.0004058247],"domain_scores_gemma":[0.9974425,0.001116797,0.0003645873,0.0007156048,0.0002460402,0.0001144788],"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":[0.00009145013,0.0003402366,0.000243266,0.0007266254,0.0002306703,0.000001062391,0.00680011,0.0001617801,0.0004103763,0.9391057,0.05103274,0.0008559096],"study_design_scores_gemma":[0.001370151,0.00007249034,0.0004314093,0.0002456043,0.000152965,0.00002694502,0.001756705,0.01156576,0.005995622,0.9707097,0.00727823,0.0003944235],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.05744451,0.0003453471,0.8825049,0.04230328,0.0004664328,0.005958982,0.00007360779,0.0004292894,0.01047366],"genre_scores_gemma":[0.06206125,0.0002677552,0.8852787,0.0002873938,0.0001113987,0.0001591679,0.000004045204,0.0001032938,0.05172697],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.04375451,"threshold_uncertainty_score":0.9992222,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W4300960744","doi":"10.1017/s0004972722001009","title":"ERDŐS–LIOUVILLE SETS","year":2022,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Fields Institute for Research in Mathematical Sciences","funders":"Division of Mathematical Sciences; Fields Institute for Research in Mathematical Sciences","keywords":"Mathematics; Combinatorics; Cardinality (data modeling); Subspace topology; Real number; Transcendental number; Discrete mathematics; Mathematical analysis; Computer science","authors":[{"name":"Taboka Chalebgwa","is_ca":true},{"name":"Sidney A. Morris","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03992858725458415,"gpt":0.2945996071183587,"spread":0.2546710198637746,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001366345,0.0002659089,0.0005451041,0.0000204679,0.0004637995,0.00003205095,0.001036237,0.0001092363,0.0231454],"category_scores_gemma":[0.0005940569,0.0001857724,0.0008923048,0.0002791264,0.0002871732,0.00001715652,0.0008984542,0.0005620518,0.0001333639],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001057928,"about_ca_system_score_gemma":0.00003726647,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001170802,"about_ca_topic_score_gemma":3.413809e-7,"domain_scores_codex":[0.9972804,0.0001995206,0.000785346,0.0003048183,0.0009553341,0.0004746065],"domain_scores_gemma":[0.9975798,0.000886604,0.0004075334,0.0009256802,0.00006507379,0.0001353199],"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":[0.000009531888,0.0007289062,0.00005987226,0.0006195116,0.0001330248,0.000001989707,0.0009742675,0.00003093427,0.0003097333,0.5469128,0.4500902,0.0001292228],"study_design_scores_gemma":[0.0004654981,0.00007224883,0.0001114936,0.00008499814,0.0001220192,0.0000559381,0.001347403,0.001382318,0.0004705,0.9128006,0.0827759,0.0003111445],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7003167,0.0000942472,0.01241314,0.1123846,0.001211569,0.005133339,0.0007305944,0.0007223276,0.1669935],"genre_scores_gemma":[0.8517249,0.000004954142,0.08415378,0.001071374,0.00008046687,0.0002105907,0.000007403757,0.0001132643,0.06263324],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3673143,"threshold_uncertainty_score":0.9777476,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2050670753","doi":"10.1017/s0004972711002474","title":"ON <i>B</i>(5,<i>k</i>) GROUPS","year":2011,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Brock University","funders":"","keywords":"Mathematics; Group (periodic table); Combinatorics; Element (criminal law); Pure mathematics; Chemistry","authors":[{"name":"Yuanlin Li","is_ca":true},{"name":"Xiaoying Pan","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.1096570594129053,"gpt":0.3112599871363839,"spread":0.2016029277234787,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.00144307,0.00026511,0.000418081,0.00002205215,0.0001541226,0.00002028895,0.001112948,0.0002026373,0.01144965],"category_scores_gemma":[0.001185012,0.0001675809,0.000713543,0.0002241976,0.0006240793,0.00001976444,0.0003178232,0.0005180771,0.001002],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005378995,"about_ca_system_score_gemma":0.00002305165,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001034,"about_ca_topic_score_gemma":3.639766e-7,"domain_scores_codex":[0.99766,0.0002265632,0.0005618034,0.000302239,0.0007272586,0.0005220902],"domain_scores_gemma":[0.9971303,0.001270258,0.0002304142,0.00113146,0.00008978511,0.0001477404],"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":[0.00003747773,0.0005732239,0.00007969959,0.0003364981,0.00008563913,0.000001538377,0.001755385,3.450055e-7,0.0003246613,0.7778885,0.2188618,0.00005526684],"study_design_scores_gemma":[0.0004331725,0.0001379344,0.0003551411,0.0002118817,0.00005897266,0.00001412934,0.0004895748,0.00001496799,0.01102503,0.9827449,0.004304843,0.0002095079],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7632929,0.00001320855,0.00269123,0.009109363,0.0003369531,0.001912337,0.00005992353,0.0003499927,0.2222341],"genre_scores_gemma":[0.8999639,0.000003838359,0.06463267,0.0007528716,0.00008927808,0.00006310163,0.000001184643,0.00009655851,0.03439665],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2145569,"threshold_uncertainty_score":0.9997758,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2114486231","doi":"10.1017/s0004972700047523","title":"On Reversible Group Rings","year":2006,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Brock University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Group ring; Ring (chemistry); Group (periodic table); Associative property; Pure mathematics; Finite group; Identity (music); Combinatorics; Group algebra; Algebra over a field; Chemistry; Physics","authors":[{"name":"Yuanlin Li","is_ca":true},{"name":"Howard E. Bell","is_ca":true},{"name":"Colin Phipps","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02897191820901078,"gpt":0.260772652570171,"spread":0.2318007343611602,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.000599331,0.000242986,0.0003874593,0.00001605421,0.0001731719,0.00003800904,0.0005623836,0.000168172,0.002110358],"category_scores_gemma":[0.0002928469,0.0001642393,0.0006433133,0.0001365807,0.0002878391,0.00002208092,0.0001490128,0.000300747,0.0003707852],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006597792,"about_ca_system_score_gemma":0.00001188856,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005365198,"about_ca_topic_score_gemma":0.000001246003,"domain_scores_codex":[0.9982162,0.00006226915,0.0005241681,0.0002806641,0.0005191509,0.0003975994],"domain_scores_gemma":[0.9984015,0.0005444506,0.0002657036,0.0006695951,0.00004639287,0.00007237712],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005536846,0.000311729,0.00009743517,0.0003270188,0.00003281485,5.177238e-7,0.0001353936,0.000005103383,0.0005023872,0.4944864,0.504073,0.00002267844],"study_design_scores_gemma":[0.0004886813,0.00005388863,0.001037816,0.0003659596,0.00007912395,0.000007816606,0.0001818279,0.00002209692,0.00820696,0.9572962,0.03201567,0.0002439513],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9400514,0.00001504174,0.001772776,0.01460026,0.000214543,0.0007442624,0.00002107119,0.0002101867,0.04237048],"genre_scores_gemma":[0.847061,0.000004661058,0.06650447,0.0006166453,0.0002751541,0.00002797135,0.000003182575,0.0000761269,0.08543079],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4720573,"threshold_uncertainty_score":0.9988018,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2157245517","doi":"10.1017/s0004972700035322","title":"Lipschitz functions with maximal Clarke subdifferentials are staunch","year":2005,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":7,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Okanagan University College; University of British Columbia, Okanagan Campus; Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Subderivative; Mathematics; Lipschitz continuity; Banach space; Expansive; Separable space; Pure mathematics; Space (punctuation); Mathematical analysis; Regular polygon; Geometry; Computer science","authors":[{"name":"Jonathan M. Borwein","is_ca":true},{"name":"Xianfu Wang","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.01726263267140209,"gpt":0.2254630836947172,"spread":0.2082004510233151,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0002755975,0.0001398494,0.0002248011,0.00001738209,0.000189695,0.00009634252,0.0006470491,0.00007935011,0.00264741],"category_scores_gemma":[0.00005178722,0.00008331709,0.0003165901,0.0002953136,0.0001075617,0.00005991241,0.0001639802,0.0001562765,0.00023371],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003847964,"about_ca_system_score_gemma":0.00003078104,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007736126,"about_ca_topic_score_gemma":0.000002097584,"domain_scores_codex":[0.9987102,0.00007301718,0.0003189498,0.0002323745,0.0004564206,0.0002090509],"domain_scores_gemma":[0.9989592,0.0001041976,0.0002253335,0.0004932004,0.0001308595,0.00008720412],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00003744436,0.002166644,0.004622655,0.0003556907,0.001132685,0.000001496787,0.002250467,0.02019008,0.0005818832,0.4192087,0.5477286,0.001723616],"study_design_scores_gemma":[0.005611645,0.0004362118,0.1181106,0.0008318537,0.001365669,0.0001372437,0.002408635,0.2551632,0.01030422,0.04976086,0.553237,0.002632964],"study_design_candidate":"not_applicable","study_design_consensus":"not_applicable","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01974685,0.00001133513,0.8305085,0.1458105,0.00007867859,0.0003166532,0.00002383029,0.0001352929,0.003368372],"genre_scores_gemma":[0.6475422,0.000004264211,0.3117045,0.001108904,0.0001209114,0.00002114686,0.000004660292,0.0000154106,0.03947793],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.6277954,"threshold_uncertainty_score":0.9982643,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2079006203","doi":"10.1017/s0004972710001711","title":"DECOMPOSING LINEAR TRANSFORMATIONS","year":2010,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Memorial University of Newfoundland","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Division ring; Unit (ring theory); Countable set; Combinatorics; Existential quantification; Ring (chemistry); Division (mathematics); Discrete mathematics; Arithmetic","authors":[{"name":"Lu Wang","is_ca":true},{"name":"Yiqiang Zhou","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03609451374322633,"gpt":0.2963036341470284,"spread":0.2602091204038021,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0006809935,0.000199014,0.0003266486,0.00001441084,0.0002403079,0.00003756556,0.0005617201,0.0002075469,0.002309024],"category_scores_gemma":[0.0003653691,0.0001339273,0.0006097204,0.0001208476,0.0003351686,0.00003788645,0.00008351666,0.0005886442,0.0001885573],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001835447,"about_ca_system_score_gemma":0.00002835483,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001039113,"about_ca_topic_score_gemma":0.000002423438,"domain_scores_codex":[0.9984491,0.0000441407,0.0005826681,0.0001799705,0.0004137712,0.0003303412],"domain_scores_gemma":[0.9986074,0.000401131,0.0002012847,0.0005945818,0.00008570567,0.0001099147],"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":[0.00001101198,0.000914813,0.0003137143,0.00148151,0.0002244695,9.011107e-7,0.005522071,0.00001520472,0.02619104,0.6875309,0.2770784,0.0007160242],"study_design_scores_gemma":[0.0008538684,0.00004264421,0.0008465457,0.0003499851,0.0002366849,0.00006721561,0.0008818464,0.000643188,0.06957906,0.8172292,0.1087591,0.0005106837],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9608552,0.000006103299,0.00760622,0.01983867,0.0003392398,0.0006352226,0.0000246187,0.0001655572,0.01052914],"genre_scores_gemma":[0.7335781,0.000004821898,0.2588005,0.0002941249,0.0002185751,0.00002192132,0.000002273347,0.00004828973,0.007031322],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2511943,"threshold_uncertainty_score":0.998603,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W3033412122","doi":"10.1017/s0004972720000477","title":"A REFORMULATION OF THE DYNAMICAL MANIN–MUMFORD CONJECTURE","year":2020,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":7,"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":"Endomorphism; Conjecture; Mathematics; Abelian group; Pure mathematics; Beal's conjecture","authors":[{"name":"Dragos Ghioca","is_ca":true},{"name":"Thomas J. Tucker","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03555894321780724,"gpt":0.270655483542954,"spread":0.2350965403251468,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005245622,0.0001984728,0.0004118312,0.000006294854,0.0001211367,0.00001202456,0.0007659158,0.000216571,0.002052924],"category_scores_gemma":[0.0009166154,0.0001037852,0.0007475328,0.0002655564,0.0004236113,0.00001814478,0.000323939,0.0003963243,0.00004740348],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003600131,"about_ca_system_score_gemma":0.00002598122,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005159004,"about_ca_topic_score_gemma":2.531062e-7,"domain_scores_codex":[0.9982992,0.0001511412,0.0006072563,0.0001977471,0.0004965284,0.0002481233],"domain_scores_gemma":[0.9983614,0.0004984547,0.0004137269,0.000577194,0.00006065642,0.00008855929],"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":[0.00007306157,0.0003990263,0.0008653415,0.002704363,0.0003567555,7.144809e-7,0.005796036,0.000053739,0.003713493,0.8918328,0.09402649,0.0001782062],"study_design_scores_gemma":[0.0008593363,0.00009915826,0.001918158,0.000379656,0.0002938448,0.00002465078,0.001671616,0.0007121172,0.02199943,0.9627427,0.009008253,0.0002911097],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9271569,0.00001113398,0.003732482,0.06323686,0.0001255125,0.000875205,0.00004218477,0.0000771046,0.004742654],"genre_scores_gemma":[0.9858372,0.000001152571,0.01003946,0.0006267045,0.00007223419,0.000007874724,0.000001307356,0.00002601715,0.003388069],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08501824,"threshold_uncertainty_score":0.9988593,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2253198932","doi":"10.1017/s0004972715001112","title":"A CLOSED FORM FOR THE DENSITY FUNCTIONS OF RANDOM WALKS IN ODD DIMENSIONS","year":2015,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Random walk; Pure mathematics; Combinatorics; Statistics","authors":[{"name":"Jonathan M. Borwein","is_ca":false},{"name":"Corwin Sinnamon","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.08208785722918291,"gpt":0.317417441300687,"spread":0.2353295840715041,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001287773,0.000165331,0.0004686725,0.00001209146,0.000119465,0.00001279354,0.0003828291,0.0001379311,0.0001714397],"category_scores_gemma":[0.005875366,0.00008910117,0.0004208116,0.000174081,0.0002397717,0.00001212062,0.0001483943,0.0002205362,0.00001569383],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000488748,"about_ca_system_score_gemma":0.00006897471,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000305952,"about_ca_topic_score_gemma":0.000007894369,"domain_scores_codex":[0.9984285,0.00005029101,0.0006645581,0.0001708016,0.0003945567,0.0002912766],"domain_scores_gemma":[0.9948084,0.00411833,0.0002694537,0.0004689485,0.0002359864,0.00009884162],"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":[0.0002414265,0.0007201641,0.00005429162,0.001094785,0.0002083117,5.655879e-7,0.00285755,0.00003986127,0.0004165632,0.7965236,0.197507,0.0003358596],"study_design_scores_gemma":[0.002285167,0.0001111486,0.0001110894,0.0002207694,0.0002880661,0.000007458077,0.002337997,0.005814163,0.0009582049,0.9853173,0.002411496,0.0001371078],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05824381,0.00004557535,0.9218989,0.01587912,0.0003339752,0.002568394,0.0001647171,0.00005201582,0.0008135075],"genre_scores_gemma":[0.8922598,0.000004649196,0.1041311,0.0001794172,0.00005407486,0.0001354001,0.000002258418,0.00003040106,0.003202899],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.834016,"threshold_uncertainty_score":0.7033786,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2072687636","doi":"10.1017/s0004972700036236","title":"The day norm and Gruenhage compacta","year":2004,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Banach Space Theory","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada; Akademie Věd České Republiky; Grantová Agentura České Republiky; University of Alberta","keywords":"Mathematics; Norm (philosophy); Convexity; Pure mathematics; Sigma; Elementary proof; Epistemology","authors":[{"name":"Marián Fabian","is_ca":false},{"name":"V. Montesinos","is_ca":true},{"name":"Václav Zizler","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02709049195087747,"gpt":0.2936257919433974,"spread":0.26653529999252,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001535736,0.0002452985,0.0003634278,0.00000732655,0.0004090397,0.00004906135,0.000650391,0.0001294642,0.0003026319],"category_scores_gemma":[0.001166601,0.0001300797,0.0003525067,0.0001203233,0.001050526,0.00002781554,0.0002886319,0.0003748666,0.00008296857],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008454479,"about_ca_system_score_gemma":0.00002815959,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009671501,"about_ca_topic_score_gemma":0.000002298322,"domain_scores_codex":[0.9983295,0.0001306679,0.0004619987,0.0002202973,0.0004281403,0.0004293979],"domain_scores_gemma":[0.9970542,0.001669077,0.0002822235,0.0008173035,0.00005836693,0.0001188872],"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":[0.00001578706,0.0002532899,0.00005428746,0.0004215906,0.0001645406,0.000001507158,0.003002537,0.00003190528,0.001058104,0.9241397,0.07057799,0.0002787273],"study_design_scores_gemma":[0.0005850159,0.00003603326,0.0003259769,0.0002107743,0.00009491613,0.00002787101,0.002042024,0.00001948235,0.004697595,0.9735794,0.01818008,0.0002008149],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7746236,0.000223072,0.03238612,0.1638495,0.0004279668,0.002921003,0.00005287927,0.0004317896,0.0250841],"genre_scores_gemma":[0.8513572,0.00003740134,0.1259006,0.0004727783,0.00009556109,0.00003389798,8.13171e-7,0.00007778417,0.02202401],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1633767,"threshold_uncertainty_score":0.5304495,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2158251557","doi":"10.1017/s0004972700035012","title":"On<i>C</i><sup>*</sup>-algebras with the approximate<i>n</i>-th root property","year":2005,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Nipissing University","funders":"Natural Sciences and Engineering Research Council of Canada; Nipissing University","keywords":"Mathematics; Commutative property; Unital; Separable space; Ideal (ethics); Quotient; Pure mathematics; Primary ideal; Discrete mathematics; Commutative ring; Algebra over a field; Combinatorics; Mathematical analysis","authors":[{"name":"Alex Chigogidze","is_ca":false},{"name":"A. Karasev","is_ca":true},{"name":"Kazuhiro Kawamura","is_ca":false},{"name":"Vesko Valov","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.033457380735707,"gpt":0.2925010516986777,"spread":0.2590436709629708,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001402779,0.0005041639,0.0006362044,0.0000221603,0.0005006964,0.0001133853,0.001645029,0.000224781,0.003004823],"category_scores_gemma":[0.0007353322,0.0002000662,0.000557929,0.0003946365,0.001091795,0.00006673649,0.0004186931,0.001017473,0.0005589801],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000166445,"about_ca_system_score_gemma":0.00009676241,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000965293,"about_ca_topic_score_gemma":0.000003353611,"domain_scores_codex":[0.9961359,0.0002893415,0.0006879013,0.0005336887,0.001470198,0.0008829787],"domain_scores_gemma":[0.9963092,0.001300105,0.0002883095,0.001676313,0.0002108637,0.0002152428],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001387537,0.00135926,0.0001182446,0.0009330118,0.00039276,0.00000366077,0.003995173,0.001313647,0.0004029557,0.2708587,0.7198747,0.0006091825],"study_design_scores_gemma":[0.006761704,0.001336714,0.0003415577,0.002249126,0.0007755133,0.0003069215,0.009583891,0.008573461,0.05522744,0.5386689,0.3734398,0.002734967],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7572405,0.0000493701,0.006989487,0.2097632,0.00006415691,0.005499343,0.00007931131,0.0004689651,0.01984556],"genre_scores_gemma":[0.8053017,0.000007388794,0.1096179,0.002366132,0.0003397862,0.0003734615,0.000003863947,0.0002356065,0.08175422],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3464348,"threshold_uncertainty_score":0.9979066,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1966886707","doi":"10.1017/s0004972700022292","title":"Generalised Bernoulli polynomials and series","year":2000,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Polytechnique Montréal","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Bernoulli polynomials; Bessel function; Series (stratigraphy); Taylor series; Generating function; Order (exchange); Discrete orthogonal polynomials; Wilson polynomials; Pure mathematics; Classical orthogonal polynomials; Orthogonal polynomials; Recurrence relation; Bessel polynomials; Difference polynomials; Bernoulli number; Gegenbauer polynomials; Euler's formula; Discrete mathematics; Combinatorics; Mathematical analysis","authors":[{"name":"Clément Frappier","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03438887908996528,"gpt":0.2866545944476889,"spread":0.2522657153577236,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005165489,0.0002947632,0.0005924237,0.00001272584,0.0002042945,0.00006305712,0.0004729519,0.0001804245,0.01161688],"category_scores_gemma":[0.0004702785,0.0001997079,0.00043015,0.0001196876,0.0008569388,0.0000699408,0.0001758054,0.0002390213,0.0001819609],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003865268,"about_ca_system_score_gemma":0.00001851186,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001567665,"about_ca_topic_score_gemma":0.000001083791,"domain_scores_codex":[0.9980155,0.0001036125,0.0007202458,0.0002887821,0.0004542028,0.0004176525],"domain_scores_gemma":[0.9983484,0.0005671288,0.0002154039,0.0006706289,0.0000584488,0.0001400027],"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":[0.00004668243,0.0005396368,0.0001192645,0.002473096,0.000315804,0.000003029246,0.003185635,0.00001696195,0.003115914,0.5927434,0.3968164,0.0006242065],"study_design_scores_gemma":[0.0004455796,0.00004045125,0.0001690849,0.0002646054,0.0001449485,0.00005809319,0.0005418368,0.00002857523,0.008796652,0.9574171,0.03180623,0.0002868519],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"other","genre_scores_codex":[0.9207999,0.0001288694,0.0009520968,0.0379467,0.0001598576,0.001619207,0.00009817535,0.0003438941,0.03795136],"genre_scores_gemma":[0.1413086,0.0001576376,0.3066541,0.0006384862,0.0002643364,0.0001032156,0.000003103855,0.0001433961,0.5507271],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7794912,"threshold_uncertainty_score":0.9892867,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1991400804","doi":"10.1017/s0004972711002279","title":"A NOTE ON NIELSEN EQUIVALENCE IN FINITELY GENERATED ABELIAN GROUPS","year":2011,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"","funders":"York University","keywords":"Mathematics; Abelian group; Rank of an abelian group; Elementary abelian group; Non-abelian group; Combinatorics; G-module; Rank (graph theory); Free abelian group; Equivalence (formal languages); Automorphism; Graph; Pure mathematics; Discrete mathematics","authors":[{"name":"Daniel Oancea","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.09031598133966928,"gpt":0.3183979921316468,"spread":0.2280820107919775,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0008419647,0.0002550953,0.0004326249,0.00002695893,0.0001102672,0.000007763478,0.0006461795,0.0002867774,0.00282058],"category_scores_gemma":[0.0006542431,0.0001734988,0.0003521561,0.0002098665,0.0005548546,0.00002346023,0.0001587035,0.0005055483,0.0002766243],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005586069,"about_ca_system_score_gemma":0.00002413015,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001508844,"about_ca_topic_score_gemma":0.000002583871,"domain_scores_codex":[0.9981706,0.0002110955,0.0005960917,0.0002973608,0.0002783033,0.0004465457],"domain_scores_gemma":[0.9981737,0.0007770964,0.000243969,0.0006680824,0.00004858659,0.00008854859],"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":[0.0001466555,0.001418687,0.0005490929,0.0006930978,0.0001133595,0.00001611014,0.009738634,0.00002527676,0.001369966,0.9575419,0.0279862,0.0004010139],"study_design_scores_gemma":[0.0006234249,0.0001140101,0.0009321124,0.0004002278,0.00005019404,0.00001533866,0.0006055227,0.00008385473,0.01232215,0.9831413,0.001448281,0.0002635528],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9503494,0.00002359634,0.005716311,0.006989369,0.0003182413,0.001175918,0.00004805078,0.0001922703,0.03518686],"genre_scores_gemma":[0.9101114,0.00001078184,0.07826226,0.0007182834,0.00005506447,0.00003678552,0.00000175855,0.00004376587,0.01075994],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07254595,"threshold_uncertainty_score":0.998091,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2150958489","doi":"10.1017/s0004972712000834","title":"CONSTRUCTION OF NORMAL NUMBERS USING THE DISTRIBUTION OF THE LARGEST PRIME FACTOR","year":2012,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Université Laval","funders":"","keywords":"Mathematics; Combinatorics; Integer (computer science); Prime number; Prime factor; Base (topology); Prime (order theory); Concatenation (mathematics); Sequence (biology); Irrational number; Distribution (mathematics); Geometry; Mathematical analysis","authors":[{"name":"Jean–Marie De Koninck","is_ca":true},{"name":"Imre Kátai","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.06684507023284411,"gpt":0.3335242325727295,"spread":0.2666791623398854,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001514399,0.0001751469,0.0003776565,0.000007217076,0.0001900713,0.0000125103,0.0007090656,0.0001606341,0.001393168],"category_scores_gemma":[0.0009615545,0.00008629002,0.0006627915,0.0002483055,0.00141907,0.00003887056,0.000332567,0.0003638654,0.00001660375],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000964775,"about_ca_system_score_gemma":0.00006129345,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006019799,"about_ca_topic_score_gemma":4.935192e-7,"domain_scores_codex":[0.99773,0.0003335592,0.0006611891,0.000123824,0.0007507898,0.0004006465],"domain_scores_gemma":[0.997546,0.0008273894,0.0006176567,0.0007671411,0.0001656843,0.00007615819],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.00007565604,0.001483204,0.05466133,0.002708506,0.001000776,1.926466e-7,0.00699878,0.00003149955,0.01340543,0.8815773,0.0378666,0.0001907542],"study_design_scores_gemma":[0.00262342,0.0001400589,0.05045423,0.002236667,0.00211523,0.0002684216,0.02008789,0.001571066,0.4939602,0.4138514,0.01160588,0.001085546],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9906531,0.00001148618,0.004658348,0.002727903,0.0001397478,0.0006374331,0.0001238441,0.00001660223,0.001031556],"genre_scores_gemma":[0.9899448,0.000002088321,0.007888729,0.00002036149,0.0000689576,0.000005654749,0.000001691972,0.0000206887,0.002047086],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4805547,"threshold_uncertainty_score":0.9995197,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W3091072354","doi":"10.1017/s0004972720000647","title":"LARGE VALUES OF <i>L</i>-FUNCTIONS ON THE 1-LINE","year":2020,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Dedekind cut; Line (geometry); Combinatorics; Order (exchange); Riemann hypothesis; Riemann zeta function; Function (biology); Pure mathematics; Geometry","authors":[{"name":"Anup B. Dixit","is_ca":true},{"name":"Kamalakshya Mahatab","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.1015781640215065,"gpt":0.3378532928759624,"spread":0.2362751288544558,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001520213,0.0001905187,0.0004211506,0.000008400812,0.0001791149,0.00001829723,0.0008746657,0.0001155339,0.007921649],"category_scores_gemma":[0.002740339,0.00009810998,0.0007293664,0.0002782558,0.0005401013,0.00001147376,0.0003138724,0.000463379,0.0004353628],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002722316,"about_ca_system_score_gemma":0.00003467035,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004157574,"about_ca_topic_score_gemma":2.074214e-7,"domain_scores_codex":[0.9978246,0.0002605414,0.0005953915,0.0002164522,0.0007603241,0.0003426643],"domain_scores_gemma":[0.996507,0.002230643,0.0002709262,0.0007431781,0.0001288878,0.0001193229],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002556258,0.0003833824,0.0000703691,0.0004545752,0.0002046372,3.914612e-7,0.001961175,0.00001053218,0.0005744266,0.4194613,0.5768412,0.00001246662],"study_design_scores_gemma":[0.0009251417,0.0002804539,0.0001178704,0.0004395963,0.0003610076,0.000007396094,0.009334095,0.001278519,0.02066818,0.9191515,0.04713135,0.0003049282],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"commentary","genre_gemma":"empirical","genre_scores_codex":[0.3816141,0.00002680009,0.02043485,0.548968,0.0001698352,0.002538874,0.0003254162,0.0002228212,0.04569923],"genre_scores_gemma":[0.9626269,0.000004493173,0.00557008,0.001727779,0.0001442562,0.00002517896,0.000001748533,0.00004750289,0.0298521],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5810127,"threshold_uncertainty_score":0.9929852,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1999881617","doi":"10.1017/s0004972708000099","title":"OUTER AUTOMORPHISM GROUPS OF CERTAIN TREE PRODUCTS OF ABELIAN GROUPS","year":2008,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":5,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Abelian group; Tree (set theory); Automorphism; Non-abelian group; Rank of an abelian group; Inner automorphism; Elementary abelian group; Automorphism group; Pure mathematics; Combinatorics; Discrete mathematics","authors":[{"name":"Y. D. Chai","is_ca":false},{"name":"Younggi Choi","is_ca":false},{"name":"Goansu Kim","is_ca":false},{"name":"C. Y. Tang","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03869099300674883,"gpt":0.2705307745244882,"spread":0.2318397815177394,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000981706,0.0002286026,0.0005449494,0.00004399074,0.0001264651,0.00001333811,0.002172783,0.0001404255,0.0002350885],"category_scores_gemma":[0.0004059496,0.0001576685,0.0005181993,0.0006260205,0.00127448,0.00008194298,0.000637078,0.0003194819,0.00005180853],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003902261,"about_ca_system_score_gemma":0.00006743288,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001688649,"about_ca_topic_score_gemma":3.390019e-7,"domain_scores_codex":[0.9973123,0.0002036895,0.0007398911,0.0003989322,0.0008807337,0.0004644327],"domain_scores_gemma":[0.9973739,0.0003663081,0.0004199758,0.00144393,0.0002779348,0.0001179685],"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":[0.00006306855,0.002000904,0.001693706,0.002589368,0.0004090606,0.00001879765,0.01060154,0.000144226,0.04517322,0.8139928,0.1215145,0.001798874],"study_design_scores_gemma":[0.002872412,0.0007760968,0.01936265,0.0009876102,0.000117843,0.0003082503,0.001048107,0.002751077,0.3563623,0.5997502,0.01455161,0.001111804],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8256052,0.0001391087,0.102315,0.06367303,0.0004300417,0.002538269,0.00006711402,0.0002818993,0.004950356],"genre_scores_gemma":[0.848074,0.00001388074,0.1450742,0.0001093592,0.00003984081,0.00001952255,0.000001110481,0.00002349695,0.006644547],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3111891,"threshold_uncertainty_score":0.6429533,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2149410667","doi":"10.1017/s0004972710001632","title":"PERFECT COLOURINGS OF ISONEMAL FABRICS BY THIN STRIPING","year":2010,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Mathematics and Applications","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Manitoba","funders":"","keywords":"Data striping; Mathematics; Combinatorics; Genus; Computer science; Botany; Operating system; Biology","authors":[{"name":"R. S. D. Thomas","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02774814093972463,"gpt":0.2896136132817982,"spread":0.2618654723420736,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001090051,0.0002410574,0.0005300777,0.00001518914,0.0001650981,0.00003092086,0.0008150005,0.0002450934,0.002317642],"category_scores_gemma":[0.0008451381,0.0001680206,0.0005942015,0.0001963792,0.0004371749,0.00001884141,0.0002387556,0.0005419138,0.00004815075],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002160501,"about_ca_system_score_gemma":0.00003620811,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002010131,"about_ca_topic_score_gemma":0.000001005192,"domain_scores_codex":[0.9980004,0.00005153752,0.0008271303,0.0002444306,0.0005395242,0.000336929],"domain_scores_gemma":[0.9973797,0.0009008669,0.0006113999,0.0008630429,0.0001336036,0.0001113987],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0000043713,0.0007518651,0.0001555857,0.001458978,0.0001114371,1.451128e-7,0.001343968,0.000002865521,0.03635251,0.187049,0.7726981,0.00007117919],"study_design_scores_gemma":[0.001578948,0.0001649882,0.0004038781,0.0008597734,0.0006132236,0.00005348301,0.002530176,0.002066303,0.2300998,0.6061144,0.1545191,0.00099598],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.97219,0.00001221277,0.005937607,0.0119416,0.0001322506,0.001214107,0.0001250469,0.0001055343,0.0083417],"genre_scores_gemma":[0.8103048,0.000004863479,0.175337,0.0001295713,0.00007272844,0.00006007834,0.000003175406,0.00005744461,0.01403029],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.618179,"threshold_uncertainty_score":0.9985944,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2142883049","doi":"10.1017/s0004972700035048","title":"Finding the group structure of elliptic curves over finite fields","year":2005,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Cryptography and Residue Arithmetic","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Killam Trusts; National Science Foundation","keywords":"Mathematics; Schoof's algorithm; Finite field; Elliptic curve; Division polynomials; Divisor (algebraic geometry); Prime (order theory); Supersingular elliptic curve; Group (periodic table); Hessian form of an elliptic curve; Field (mathematics); Polynomial; Twists of curves; Pure mathematics; Discrete mathematics; Combinatorics; Mathematical analysis; Quarter period","authors":[{"name":"John Friedlander","is_ca":true},{"name":"Carl Pomerance","is_ca":false},{"name":"Igor E. Shparlinski","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.01519964463907791,"gpt":0.2434240313792095,"spread":0.2282243867401316,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003344287,0.0001379899,0.0002202191,0.00001275742,0.0001366992,0.00003464415,0.001297906,0.0001128436,0.0007364372],"category_scores_gemma":[0.0001033186,0.00007146788,0.0004773235,0.0002755472,0.000308932,0.00003678066,0.0002873762,0.0002854211,0.00001509941],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001077175,"about_ca_system_score_gemma":0.00001308535,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001354681,"about_ca_topic_score_gemma":0.00000157574,"domain_scores_codex":[0.9987537,0.00008305353,0.000357921,0.0001797107,0.0003888603,0.000236755],"domain_scores_gemma":[0.9984875,0.0005438082,0.0001976275,0.0006898673,0.00003512334,0.00004602132],"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":[0.00001241991,0.0007016222,0.002090147,0.003169745,0.0005465056,0.000001752259,0.008935322,0.001899066,0.00609298,0.5587549,0.4138437,0.003951913],"study_design_scores_gemma":[0.00348556,0.0005974824,0.09059216,0.006899206,0.0008823927,0.0001524068,0.001655686,0.03528019,0.105053,0.5400319,0.2130663,0.002303665],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5974538,0.001410957,0.1666797,0.2286755,0.0006862888,0.001865251,0.00006494749,0.0002083227,0.002955226],"genre_scores_gemma":[0.9581289,0.0000481058,0.03982993,0.001030412,0.00006042086,0.000003494065,5.278513e-7,0.000007394986,0.00089084],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3606751,"threshold_uncertainty_score":0.8063471,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W3195490484","doi":"10.1017/s0004972721000976","title":"ON FINE SELMER GROUPS AND SIGNED SELMER GROUPS OF ELLIPTIC MODULAR FORMS","year":2022,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Université Laval","funders":"","keywords":"Mathematics; Coprime integers; Modular form; Divisor (algebraic geometry); Prime (order theory); Abelian group; Context (archaeology); Pure mathematics; Elliptic curve; Algebra over a field; Discrete mathematics; Combinatorics","authors":[{"name":"Antonio Lei","is_ca":true},{"name":"Meng Fai Lim","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02142951374256583,"gpt":0.2514640078522473,"spread":0.2300344941096815,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001489908,0.0002938508,0.0006125978,0.00003114824,0.0002885806,0.00001499756,0.0005885443,0.0001402261,0.007032807],"category_scores_gemma":[0.0004004764,0.0002042838,0.0005429109,0.000279077,0.0004096174,0.00002542112,0.0004735802,0.0004799893,0.00004485382],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005788707,"about_ca_system_score_gemma":0.00001851375,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005803573,"about_ca_topic_score_gemma":1.467698e-7,"domain_scores_codex":[0.997613,0.0002203592,0.0007052264,0.0003211605,0.0007448434,0.0003954563],"domain_scores_gemma":[0.9975064,0.001206588,0.0004152608,0.0007093159,0.00005206375,0.0001103856],"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":[0.0001173857,0.001315048,0.0001683715,0.001709836,0.0004359551,0.000002814345,0.003426764,0.0001057607,0.003789352,0.9378195,0.0510093,0.00009986223],"study_design_scores_gemma":[0.0009592802,0.0003076252,0.0003148549,0.0001463535,0.0002253462,0.00003951998,0.002128208,0.0002008599,0.01069727,0.9829661,0.001702468,0.0003121747],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9934903,0.00002713909,0.001027302,0.00300494,0.00007989223,0.0005834477,0.00005049674,0.00004843858,0.001688077],"genre_scores_gemma":[0.9845419,0.000002985871,0.006310806,0.0002710614,0.00003740395,0.00005293901,0.000004197557,0.00004772217,0.008730994],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04930683,"threshold_uncertainty_score":0.9938749,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W4293223910","doi":"10.1017/s0004972722000764","title":"THE SECOND SHIFTED DIFFERENCE OF PARTITIONS AND ITS APPLICATIONS","year":2022,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Manitoba","funders":"","keywords":"Mathematics; Partition (number theory); Convexity; Combinatorics; Rank (graph theory); Partition function (quantum field theory); Function (biology); Upper and lower bounds; Mathematical analysis; Physics","authors":[{"name":"Kevin Gomez","is_ca":false},{"name":"Joshua Males","is_ca":true},{"name":"Larry Rolen","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04381526815692646,"gpt":0.2986842874427026,"spread":0.2548690192857762,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0006290193,0.0001586859,0.0003277697,0.00001091158,0.0006626553,0.0000251628,0.0006377238,0.00005425642,0.002601107],"category_scores_gemma":[0.000567883,0.00009975633,0.0002843617,0.0001847956,0.0005639155,0.00001786837,0.0005856229,0.0003170182,0.00001513328],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003959992,"about_ca_system_score_gemma":0.00002543477,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002150215,"about_ca_topic_score_gemma":0.000001983921,"domain_scores_codex":[0.9983113,0.0001323695,0.0006279592,0.0001850596,0.0004791571,0.000264146],"domain_scores_gemma":[0.9964997,0.002381708,0.0003875007,0.0005751532,0.00008618776,0.00006976262],"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":[0.000005172893,0.0002775207,0.00002413459,0.0009210614,0.0000884379,1.404239e-7,0.0008794237,0.000006947232,0.0009902682,0.9723012,0.02446927,0.00003636822],"study_design_scores_gemma":[0.0001831385,0.00002971928,0.0001271817,0.00005544508,0.0000795153,0.00001232606,0.00190501,0.000128856,0.003112763,0.9719239,0.02232744,0.0001146497],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8759288,0.0008956122,0.01755057,0.06367549,0.0003623118,0.008656604,0.001345394,0.0004289194,0.03115627],"genre_scores_gemma":[0.8694482,0.00002934034,0.01865316,0.0001328926,0.00004043575,0.0009159207,0.000002712362,0.00004850127,0.1107289],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0795726,"threshold_uncertainty_score":0.9983106,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2024389767","doi":"10.1017/s0004972711003042","title":"HELICOIDAL MINIMAL SURFACES IN ℍ<sup>2</sup>×ℝ","year":2011,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","field":"Engineering","cited_by":4,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Invariant (physics); Pure mathematics; Minimal surface; Surface (topology); Conjugate; Mathematical analysis; Geometry; Mathematical physics","authors":[{"name":"Young‐Wook Kim","is_ca":true},{"name":"Sung-Eun Koh","is_ca":false},{"name":"Heayong Shin","is_ca":false},{"name":"Seong-Deog Yang","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.01825758795763855,"gpt":0.2224374870673145,"spread":0.204179899109676,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.000257695,0.0001386632,0.0002313512,0.000007814691,0.00005845155,0.00001023616,0.0003662843,0.00008616287,0.002634525],"category_scores_gemma":[0.00003494027,0.00008657467,0.000159727,0.0001680974,0.0004495772,0.00001412784,0.0001286274,0.0001480607,0.0001042442],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001843581,"about_ca_system_score_gemma":0.000002792422,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009084918,"about_ca_topic_score_gemma":2.894275e-7,"domain_scores_codex":[0.9990584,0.00001721241,0.0002969538,0.0001341379,0.0001781878,0.0003151702],"domain_scores_gemma":[0.9996409,0.00007072902,0.00003254487,0.0001847091,0.00001240591,0.00005873906],"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":[0.0001464775,0.001465923,0.005407808,0.003673477,0.0004624772,0.00001196952,0.0381535,0.04044758,0.01009177,0.8114076,0.08463955,0.004091832],"study_design_scores_gemma":[0.001734106,0.0002485232,0.010097,0.0007023507,0.0001105835,0.00002141729,0.01418289,0.01593341,0.06115386,0.7693125,0.1249136,0.00158981],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9661733,0.00003771923,0.0006357207,0.0008598408,0.0001149592,0.0002203239,0.00001613017,0.00007561572,0.03186642],"genre_scores_gemma":[0.9868671,0.0000218791,0.01210526,0.00005252389,0.00003391888,0.00001117968,2.895124e-7,0.00001117962,0.0008967164],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05106209,"threshold_uncertainty_score":0.9982772,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2146940934","doi":"10.1017/s0004972700037953","title":"Powerful numbers in short intervals","year":2005,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Université Laval","funders":"Natural Sciences and Engineering Research Council of Canada; Consejo Nacional de Ciencia y Tecnología","keywords":"Mathematics; Integer (computer science); Interval (graph theory); Conjecture; Combinatorics; Discrete mathematics","authors":[{"name":"Jean–Marie De Koninck","is_ca":true},{"name":"Florian Luca","is_ca":false},{"name":"Igor E. Shparlinski","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.05975522520348473,"gpt":0.3543378579093029,"spread":0.2945826327058181,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002111896,0.0002386129,0.0005193254,0.0000269978,0.00006072531,0.00003123242,0.0009641089,0.0001923733,0.009500501],"category_scores_gemma":[0.0009190777,0.0001641348,0.0006553379,0.0002616958,0.0004866783,0.00003385312,0.0003548632,0.0005266385,0.0007172021],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001744331,"about_ca_system_score_gemma":0.00003618495,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002657391,"about_ca_topic_score_gemma":0.000008631717,"domain_scores_codex":[0.9974501,0.0002073298,0.0008142815,0.0002896068,0.0006924896,0.0005461636],"domain_scores_gemma":[0.9980268,0.0008516082,0.0001002433,0.0008104998,0.00007677892,0.0001340405],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00004463811,0.001391066,0.003990444,0.0009640685,0.0003008621,0.000004766189,0.004817283,0.00003143908,0.0008513053,0.242194,0.7446623,0.000747856],"study_design_scores_gemma":[0.001598389,0.0001013299,0.002391854,0.001379161,0.0002228855,0.0000902654,0.005216682,0.0009862568,0.01768387,0.8612897,0.1081511,0.0008884922],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8657971,0.00001923855,0.001569526,0.05162047,0.00009720498,0.001214003,0.00001995302,0.0001175842,0.07954492],"genre_scores_gemma":[0.9155173,0.000005056263,0.03330041,0.0003399643,0.0000973854,0.00001978488,8.481531e-7,0.0000507067,0.05066853],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6365112,"threshold_uncertainty_score":0.991405,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1985795385","doi":"10.1017/s000497270900094x","title":"EHRLICH’S THEOREM FOR GROUPS","year":2010,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Calgary; Brock University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Endomorphism; Mathematics; Automorphism; Unit (ring theory); Group (periodic table); Combinatorics; Discrete mathematics; Pure mathematics; Mathematics education","authors":[{"name":"Yuanlin Li","is_ca":true},{"name":"W. K. Nicholson","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03657960405824517,"gpt":0.2881412886544986,"spread":0.2515616845962534,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001123343,0.0002567107,0.0004418774,0.00001210813,0.0002068788,0.00004743644,0.0008084223,0.0002529076,0.002083432],"category_scores_gemma":[0.001165212,0.0001637489,0.0008992891,0.00009259699,0.0004940287,0.0000239897,0.0001688243,0.0004327229,0.0001154247],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002101866,"about_ca_system_score_gemma":0.00002619852,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006419505,"about_ca_topic_score_gemma":0.000001989864,"domain_scores_codex":[0.9982733,0.00004638954,0.0005653448,0.0002888816,0.0003777149,0.0004483576],"domain_scores_gemma":[0.9976255,0.001000857,0.0002904529,0.0008543823,0.0001070743,0.0001217197],"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":[0.000008427251,0.0002451575,0.00007056809,0.0005394607,0.00007678364,1.634268e-7,0.0008019044,4.350101e-7,0.003814341,0.761558,0.2327169,0.0001678826],"study_design_scores_gemma":[0.0005105977,0.00003652031,0.0002810725,0.0001043105,0.000110851,0.00001475515,0.0004208343,0.0000607651,0.01586975,0.9219815,0.06037701,0.0002320448],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.954353,0.000009371636,0.007423212,0.02660154,0.000641796,0.001700217,0.00006137264,0.0002123074,0.008997205],"genre_scores_gemma":[0.7709116,0.000003432119,0.2033108,0.0005366158,0.0004989952,0.0001136,0.000003121071,0.00009152877,0.02453026],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1958876,"threshold_uncertainty_score":0.9988288,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2131677444","doi":"10.1017/s0004972700035784","title":"ABS-type methods for solving full row rank linear systems using a new rank two update","year":2004,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"","funders":"Sharif University of Technology; York University","keywords":"Mathematics; Rank (graph theory); Dimension (graph theory); Type (biology); Matrix (chemical analysis); System of linear equations; Linear equation; Class (philosophy); Applied mathematics; Augmented matrix; Linear system; Combinatorics; Mathematical analysis; Square matrix; Symmetric matrix; Eigenvalues and eigenvectors","authors":[{"name":"Keyvan Amini","is_ca":false},{"name":"Nezam Mahdavi‐Amiri","is_ca":false},{"name":"M. Reza Peyghami","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04777071579681103,"gpt":0.3429566183003342,"spread":0.2951859025035232,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002118431,0.0002607653,0.0004944379,0.00001971766,0.0002690549,0.0001477216,0.00141638,0.0001481786,0.0001645575],"category_scores_gemma":[0.0002424543,0.0001840949,0.000608416,0.0002998443,0.00015494,0.00007912789,0.0003407488,0.0002461611,0.00007269401],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000770047,"about_ca_system_score_gemma":0.00009514089,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005926914,"about_ca_topic_score_gemma":1.612313e-7,"domain_scores_codex":[0.9980933,0.0001088123,0.0006127373,0.0003832787,0.0003042854,0.0004976068],"domain_scores_gemma":[0.9981589,0.0004570186,0.0003173678,0.0007661112,0.0001235115,0.0001770768],"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":[0.00005276802,0.0002674772,0.00000338193,0.001241836,0.0003067274,0.000002459989,0.002253712,0.01608844,0.01478767,0.9518635,0.01111435,0.002017635],"study_design_scores_gemma":[0.003280037,0.000159883,0.000005315696,0.0008705786,0.0002248253,0.0001496252,0.0003410998,0.178754,0.02940316,0.747296,0.03880234,0.0007131619],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.003458958,0.00009858628,0.9879319,0.007081187,0.0005251331,0.0006705255,0.000004654152,0.0001032242,0.0001258466],"genre_scores_gemma":[0.01063802,0.000006405015,0.9850883,0.0003007942,0.000277549,0.00001197006,0.000001020084,0.00002792096,0.003648002],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.2045676,"threshold_uncertainty_score":0.7507172,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W4304806462","doi":"10.1017/s0004972722001150","title":"A REMARK ON THE GEOMETRIC INTERPRETATION OF THE A3W CONDITION FROM OPTIMAL TRANSPORT","year":2022,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Fields Institute for Research in Mathematical Sciences","funders":"Division of Mathematical Sciences; Fields Institute for Research in Mathematical Sciences","keywords":"Interpretation (philosophy); Mathematics; Calculus (dental); Mathematical economics; Computer science","authors":[{"name":"Cale Rankin","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02612102788418904,"gpt":0.2617508790605066,"spread":0.2356298511763175,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001476674,0.0001964128,0.000433399,0.00004308457,0.0003308822,0.00001844151,0.0009997954,0.0001002251,0.009340711],"category_scores_gemma":[0.0008693036,0.0000965392,0.001172445,0.001187867,0.0002532976,0.00001678005,0.0001941603,0.0005678692,0.00002283102],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008227638,"about_ca_system_score_gemma":0.00003124829,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004466383,"about_ca_topic_score_gemma":0.000001046266,"domain_scores_codex":[0.9974228,0.0003239978,0.0007046912,0.0002335518,0.001089868,0.0002251369],"domain_scores_gemma":[0.9967697,0.001631146,0.0006391401,0.0008279273,0.00009054893,0.0000414905],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001852303,0.002749925,0.001890959,0.0007744369,0.002015603,0.000001934357,0.01134935,0.004020638,0.001449025,0.1540264,0.8208128,0.0007237684],"study_design_scores_gemma":[0.004141568,0.0009979241,0.06299642,0.001617576,0.005907522,0.00004958145,0.04543618,0.0128612,0.02276884,0.7531943,0.08819861,0.001830313],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9728667,0.00002917634,0.004267661,0.01910666,0.0001860951,0.000858406,0.0002095563,0.00002971029,0.002446],"genre_scores_gemma":[0.9916949,0.000002725661,0.003234035,0.0004250926,0.0000386666,0.00006095674,0.000009664648,0.00002162094,0.004512383],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7326141,"threshold_uncertainty_score":0.9915649,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W4312117129","doi":"10.1017/s000497272200140x","title":"SIN, COS, EXP AND LOG OF LIOUVILLE NUMBERS","year":2022,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":3,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"Fields Institute for Research in Mathematical Sciences","funders":"Division of Mathematical Sciences; Fields Institute for Research in Mathematical Sciences","keywords":"Mathematics; Transcendental number; Hyperbolic function; Alpha (finance); Inverse trigonometric functions; Transcendental function; Trigonometric functions; Transcendental equation; Trigonometry; Combinatorics; Pythagorean trigonometric identity; Pure mathematics; Mathematical analysis; Geometry; Differential equation; Polynomial; Statistics","authors":[{"name":"Taboka Chalebgwa","is_ca":true},{"name":"Sidney A. Morris","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.01173015624292502,"gpt":0.2498994462813277,"spread":0.2381692900384027,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0001936672,0.0001077031,0.0002448201,0.000004769953,0.0002042098,0.000007662732,0.0002709196,0.00002256923,0.006161694],"category_scores_gemma":[0.00001849789,0.00007864658,0.0002243219,0.00011488,0.000336968,0.000009660673,0.0003170292,0.0001675109,0.0000128968],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001294989,"about_ca_system_score_gemma":0.00001215497,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001856018,"about_ca_topic_score_gemma":3.138142e-8,"domain_scores_codex":[0.9991406,0.00003779471,0.0003122136,0.0001383271,0.0002055704,0.00016548],"domain_scores_gemma":[0.9991927,0.0002165013,0.0001935882,0.0003149004,0.000028843,0.0000535135],"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":[0.000004648154,0.0002839035,0.0002492497,0.0001204606,0.00006504934,4.458699e-8,0.0006365874,0.00007340743,0.0006904901,0.9579982,0.03959265,0.0002853113],"study_design_scores_gemma":[0.0003958137,0.00004182172,0.000117655,0.00004534823,0.00007157004,0.000003212153,0.007267028,0.00007329696,0.005673484,0.8963128,0.08982978,0.0001681283],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8185809,0.00009806539,0.04015351,0.03506212,0.0002015668,0.002527522,0.0008372545,0.0001102301,0.1024289],"genre_scores_gemma":[0.9776937,0.00000146957,0.01466282,0.00008278823,0.00003053447,0.00007232872,0.000003880926,0.00001491527,0.007437545],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1591129,"threshold_uncertainty_score":0.9947468,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2975307756","doi":"10.1017/s0004972719001023","title":"PRIME-UNIVERSAL QUADRATIC FORMS AND","year":2019,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Prime (order theory); Ternary operation; Prime number; Diagonal; Quadratic equation; Combinatorics; Quadratic form (statistics); Quadratic residue; Binary quadratic form; Isotropic quadratic form; Discrete mathematics; Quadratic function; Geometry; Computer science","authors":[{"name":"Greg Doyle","is_ca":true},{"name":"Kenneth S. Williams","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03519635512307036,"gpt":0.3053694869443363,"spread":0.270173131821266,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0009870842,0.000182601,0.00039809,0.000014176,0.00009259996,0.00003288361,0.0005060066,0.0001414072,0.005531769],"category_scores_gemma":[0.0003649362,0.0001131863,0.0003486576,0.0001279581,0.0004221063,0.00003078801,0.0003302663,0.0003061485,0.0004887893],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005530595,"about_ca_system_score_gemma":0.00003555657,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001140475,"about_ca_topic_score_gemma":4.357993e-7,"domain_scores_codex":[0.9984039,0.0001038083,0.0003835463,0.000232674,0.0005159141,0.000360156],"domain_scores_gemma":[0.9981648,0.0008084646,0.0001776208,0.0006678474,0.0000644074,0.0001168174],"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":[0.00003174997,0.0003322538,0.002438452,0.001775858,0.0003160241,0.000001310245,0.002286278,0.000002121253,0.001639844,0.9055507,0.08545721,0.0001682481],"study_design_scores_gemma":[0.001039621,0.0001049654,0.0008466908,0.0003789965,0.0001612113,0.00003768703,0.003825077,0.0005540721,0.004150447,0.9788628,0.009716664,0.0003217697],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9610297,0.00001146104,0.001401256,0.01082545,0.00005804378,0.001073778,0.0000104692,0.00007052747,0.02551929],"genre_scores_gemma":[0.8808818,0.000004157459,0.019089,0.0001258164,0.00002893219,0.000008343483,6.994071e-7,0.00003748623,0.09982374],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08014789,"threshold_uncertainty_score":0.9953773,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2981650987","doi":"10.1017/s0004972719001102","title":"A NOTE ON NORMALISED HEAT DIFFUSION FOR GRAPHS","year":2019,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Markov Chains and Monte Carlo Methods","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"McGill University","funders":"","keywords":"Mathematics; Eigenvalues and eigenvectors; Monotonic function; Heat equation; Diffusion; Laplace operator; Heat kernel; Combinatorics; Mathematical analysis; Thermodynamics; Physics","authors":[{"name":"Bogdan Nica","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.04348557945156247,"gpt":0.3252619150649488,"spread":0.2817763356133863,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00115452,0.0002561002,0.0005145678,0.00001802648,0.0001168801,0.00002427569,0.0004819561,0.0002182132,0.0007359969],"category_scores_gemma":[0.0005835039,0.0001581918,0.001095583,0.0001149792,0.0001326735,0.00001311798,0.0001447879,0.000241539,0.000007380484],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004959136,"about_ca_system_score_gemma":0.00001897164,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009454111,"about_ca_topic_score_gemma":5.288454e-7,"domain_scores_codex":[0.998255,0.0001235777,0.0005152246,0.0002914959,0.0004274783,0.0003872574],"domain_scores_gemma":[0.9972991,0.001512166,0.0001809838,0.0008115355,0.00009161751,0.0001046298],"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":[0.0002149975,0.001159135,0.0003245531,0.004797827,0.0001896548,6.807478e-7,0.002633802,0.00002697907,0.02184993,0.5501917,0.4179467,0.0006640151],"study_design_scores_gemma":[0.00738857,0.001042122,0.0005051222,0.002059188,0.0005876581,0.00002562625,0.00198698,0.004063479,0.06499543,0.6667553,0.249167,0.00142349],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9348082,0.00001138996,0.01444101,0.02649619,0.0006673299,0.004198888,0.0001156883,0.000161983,0.01909929],"genre_scores_gemma":[0.5721449,0.000009064669,0.3483993,0.001791969,0.0001671767,0.0001770481,0.000006998182,0.0001253582,0.07717824],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3626634,"threshold_uncertainty_score":0.805865,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2125109278","doi":"10.1017/s0004972700034298","title":"On biorthogonal systems and Maxur's intersection property","year":2004,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Advanced Banach Space Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Intersection (aeronautics); Banach space; Property (philosophy); Biorthogonal system; Basis (linear algebra); Subspace topology; Pure mathematics; Linear subspace; Discrete mathematics; Mathematical analysis; Geometry","authors":[{"name":"Jan Rychtář","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.03397699850961947,"gpt":0.284553591099,"spread":0.2505765925893805,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005647397,0.0002181322,0.0003380949,0.00001599915,0.0001286837,0.00002859309,0.0002599702,0.0001439596,0.0002368572],"category_scores_gemma":[0.0004483039,0.0001152114,0.000262405,0.00009865805,0.0004123593,0.00002439662,0.0001297125,0.0002896108,0.00007399864],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001283061,"about_ca_system_score_gemma":0.00002211434,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002262859,"about_ca_topic_score_gemma":8.781011e-7,"domain_scores_codex":[0.9986461,0.00008216073,0.0003881042,0.0002467914,0.0003631682,0.000273698],"domain_scores_gemma":[0.9988549,0.0003157784,0.0002275486,0.0004595849,0.0000541675,0.00008803171],"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":[0.00005401382,0.0006316534,0.00004026343,0.001267661,0.000155862,0.000002014511,0.001390551,0.0002799978,0.0015808,0.9626719,0.03179629,0.0001289964],"study_design_scores_gemma":[0.001048495,0.0002321289,0.0001415918,0.001127739,0.0001124751,0.00008590241,0.001917871,0.00008294151,0.004343009,0.986284,0.00431914,0.0003047634],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9490052,0.0000341196,0.02243258,0.01976919,0.0003955338,0.001897509,0.00003556145,0.0002598015,0.006170484],"genre_scores_gemma":[0.9612008,0.000004772245,0.02559164,0.0001765054,0.00007119328,0.00003874767,7.909435e-7,0.00004545084,0.01287005],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02747715,"threshold_uncertainty_score":0.4698183,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W4386561681","doi":"10.1017/s0004972723000898","title":"THE MORDELL–LANG CONJECTURE FOR SEMIABELIAN VARIETIES DEFINED OVER FIELDS OF POSITIVE CHARACTERISTIC","year":2023,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":3,"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":"Subvariety; Mathematics; Algebraically closed field; Conjecture; Prime (order theory); Intersection (aeronautics); Variety (cybernetics); Pure mathematics; Field (mathematics); Combinatorics; Statistics","authors":[{"name":"Dragos Ghioca","is_ca":true},{"name":"Yang She","is_ca":false}],"retraction":null,"screen_n_in":null,"score":{"opus":0.02681460196918222,"gpt":0.2852713293521977,"spread":0.2584567273830154,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001183615,0.0002133513,0.0004264497,0.00002016191,0.0002823512,0.00002824706,0.0005443297,0.0002393678,0.0006011197],"category_scores_gemma":[0.001394536,0.0001215699,0.0006102354,0.0003101396,0.0004581599,0.00001430991,0.0001847438,0.0002687128,0.00004264503],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002370695,"about_ca_system_score_gemma":0.00003001272,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001022986,"about_ca_topic_score_gemma":6.944258e-7,"domain_scores_codex":[0.9984219,0.0001110704,0.000554465,0.0001910699,0.0003431756,0.00037829],"domain_scores_gemma":[0.9947405,0.004196834,0.0003564715,0.0005408665,0.0001062034,0.00005911218],"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":[0.0001068574,0.0001734955,0.0001226648,0.001812674,0.0005012805,9.117098e-7,0.004698887,0.00001072069,0.0008210423,0.61174,0.3798716,0.000139877],"study_design_scores_gemma":[0.0005812217,0.0001059244,0.001341999,0.0002872298,0.0002420085,0.00000881885,0.002200516,0.0002405882,0.007457469,0.9765837,0.0107231,0.0002274327],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9515036,0.00005155225,0.005596561,0.0361348,0.0005332657,0.00223078,0.0003959537,0.0002784725,0.00327497],"genre_scores_gemma":[0.9479545,0.0000211468,0.007025606,0.0003578842,0.0001383941,0.00009400692,0.00001528555,0.00005674501,0.0443364],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3691485,"threshold_uncertainty_score":0.6581839,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W1963782883","doi":"10.1017/s0004972711002127","title":"EXOTIC LEFT-ORDERINGS OF THE FREE GROUPS FROM THE DEHORNOY ORDERING","year":2011,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Mathematics; Combinatorics; Free group; Braid group; Group (periodic table); Regular polygon; Geometry","authors":[{"name":"Adam Clay","is_ca":true}],"retraction":null,"screen_n_in":null,"score":{"opus":0.07597466627204683,"gpt":0.2530108331142087,"spread":0.1770361668421619,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007823749,0.000261571,0.0004969163,0.00001286338,0.0002181758,0.00001653215,0.002150551,0.0002110668,0.005424183],"category_scores_gemma":[0.001996257,0.0001248886,0.0007412808,0.0002877123,0.0009446774,0.0000189143,0.0009273139,0.0004499287,0.0000590958],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003039003,"about_ca_system_score_gemma":0.00003280341,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000252874,"about_ca_topic_score_gemma":0.00001169429,"domain_scores_codex":[0.997943,0.0001684456,0.0007213764,0.0002558785,0.0004987002,0.0004125909],"domain_scores_gemma":[0.9963976,0.00142112,0.0004939468,0.001537973,0.00008058321,0.00006875996],"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":[0.00004366308,0.001390876,0.01235354,0.001396572,0.001140163,0.000003048542,0.02964165,0.0000108751,0.001637161,0.55577,0.3961358,0.0004766782],"study_design_scores_gemma":[0.0006297735,0.00005206139,0.0219556,0.000315456,0.0003382559,0.00003107782,0.004699392,0.00003337762,0.006495246,0.9601602,0.005028039,0.0002615499],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9770939,0.00005399504,0.002317563,0.01505211,0.0003033893,0.0007109209,0.00004002356,0.00006321038,0.004364926],"genre_scores_gemma":[0.965753,0.000007502562,0.02942455,0.0003501167,0.00007965491,0.00001360106,5.350835e-7,0.00003925878,0.004331737],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4043902,"threshold_uncertainty_score":0.995485,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W2912854712","doi":"10.1017/s0004972718001648","title":"THE ERROR TERM IN THE SATO–TATE THEOREM OF BIRCH","year":2019,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"Queen's University","funders":"","keywords":"Term (time); Measure (data warehouse); Elliptic curve; Calculus (dental); Type (biology)","authors":[],"retraction":null,"screen_n_in":null,"score":{"opus":0.0320728609387014,"gpt":0.2944586873366772,"spread":0.2623858263979758,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00403714,0.0002388634,0.0004557703,0.00001633141,0.000163974,0.00003264222,0.00157673,0.000169841,0.001232736],"category_scores_gemma":[0.0006644044,0.0001056311,0.0006453068,0.0002925727,0.0007544291,0.00002136213,0.0002486097,0.0005003621,0.0002483742],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002985803,"about_ca_system_score_gemma":0.00003070559,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001404392,"about_ca_topic_score_gemma":0.000001508035,"domain_scores_codex":[0.9974352,0.0004736443,0.000783274,0.0002240163,0.0006464398,0.0004374567],"domain_scores_gemma":[0.9943029,0.003918945,0.0004276403,0.00123823,0.0000654844,0.00004677951],"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":[0.00004574099,0.0005123769,0.002514967,0.001139015,0.0001925066,0.000001051562,0.008714987,0.000006255028,0.0007878874,0.9451748,0.04061848,0.000291911],"study_design_scores_gemma":[0.0006612226,0.00007085052,0.004415176,0.0003366335,0.00009930817,0.00002528691,0.01225971,0.00003709792,0.003991779,0.9696898,0.008200068,0.0002130893],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9764929,0.00002854269,0.00007327202,0.01356099,0.000122816,0.0009116235,0.00001212192,0.00002417926,0.008773557],"genre_scores_gemma":[0.9853025,0.00001054076,0.002063357,0.0002712417,0.0000409474,0.00002830069,7.625176e-7,0.00002959162,0.01225276],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03241841,"threshold_uncertainty_score":0.9996803,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null}]}