{"id":"W4379742226","doi":"10.1017/9781009089005.009","title":"Integers and Divisibility","year":2023,"lang":"en","type":"book-chapter","venue":"Cambridge University Press eBooks","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematical proof; Cardinality (data modeling); Mathematics education; Focus (optics); Computer science; Divisibility rule; Process (computing); Perspective (graphical); Mathematics; Artificial intelligence; Programming language; Discrete mathematics","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003975528,0.0003638259,0.0005343414,0.0001539283,0.0002159909,0.00002482023,0.0003548774,0.0003695764,0.00001057167],"category_scores_gemma":[0.0001143497,0.0004107661,0.0001966896,0.000006392439,0.0004781211,0.00005731696,0.0004029535,0.000498204,0.00004481214],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001547706,"about_ca_system_score_gemma":0.00005443135,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001133554,"about_ca_topic_score_gemma":0.000002851559,"domain_scores_codex":[0.9987752,0.00005513676,0.0002369092,0.0004638879,0.0002422616,0.0002266077],"domain_scores_gemma":[0.9982359,0.0005813324,0.0002401407,0.0006795427,0.00009209802,0.0001709643],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0000367067,0.00001033524,3.346699e-7,0.0004965888,0.000126483,0.0001639478,0.0002347272,6.136752e-8,0.000005064605,0.9671856,0.03117497,0.0005652489],"study_design_scores_gemma":[0.0004669951,0.0000552686,0.000002478286,0.0004683138,0.000431909,0.00002030839,0.0001322277,0.00003352856,0.0000577302,0.04159956,0.9560953,0.0006364218],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.0007381444,0.00003280301,0.0005995803,0.000008659393,0.0002218774,0.0003654286,0.0001726685,0.0003775943,0.9974833],"genre_scores_gemma":[0.0005444532,0.00003873184,0.0004348271,0.00001679105,0.00006103947,5.616878e-7,0.00001101459,0.00007935634,0.9988132],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.925586,"threshold_uncertainty_score":0.9998344,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06141939431663986,"score_gpt":0.2382363696463585,"score_spread":0.1768169753297186,"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."}}