{"id":"W2029461183","doi":"10.1515/crelle-2012-0064","title":"On the number of integers in a generalized multiplication table","year":2012,"lang":"en","type":"article","venue":"Journal für die reine und angewandte Mathematik (Crelles Journal)","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Multiplication (music); Table (database); Order (exchange); Natural number; Multiplication algorithm; Prime number","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002550441,0.00073743,0.001294597,0.001537676,0.001861009,0.005708166,0.001254699,0.001301559,0.009074384],"category_scores_gemma":[0.01185017,0.0006309105,0.001024263,0.002409067,0.003221622,0.009390821,0.002372432,0.002090543,0.001059436],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001914921,"about_ca_system_score_gemma":0.0008380297,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000974768,"about_ca_topic_score_gemma":0.0007501571,"domain_scores_codex":[0.9979469,0.0006852762,0.0001375349,0.0005538264,0.000410188,0.0002662953],"domain_scores_gemma":[0.9929335,0.004863929,0.0008285298,0.0004940833,0.000355422,0.0005244859],"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":[0.0003558443,0.00003788363,0.001559896,0.0001861988,0.00003839718,0.0002384298,0.0003282645,0.009684138,0.001017431,0.9653089,0.005102555,0.01614213],"study_design_scores_gemma":[0.00006627825,0.00005983625,0.0004048772,0.0000444714,0.00002955459,0.0002268441,0.0001293574,0.02589319,0.0006938535,0.9658792,0.006544371,0.00002805632],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7331956,0.002656754,0.1937838,0.005674905,0.0005705061,0.0001012431,0.001354438,0.0004953982,0.06216739],"genre_scores_gemma":[0.9412084,0.0007402631,0.03971013,0.00056825,0.0004492583,0.0001023668,0.0009940234,0.0001307031,0.01609655],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009074384,"threshold_uncertainty_score":0.03035688,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0380263259884183,"score_gpt":0.3443773132782273,"score_spread":0.306350987289809,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}