{"id":"W4379742042","doi":"10.1017/9781009089005.012","title":"Elementary Combinatorics","year":2023,"lang":"en","type":"book-chapter","venue":"Cambridge University Press eBooks","topic":"Advanced Mathematical Theories","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; Perspective (graphical); Process (computing); Mathematics; Artificial intelligence; Programming language","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":[0.0002709954,0.0009041241,0.0005862869,0.001439909,0.001501641,0.004766621,0.001034899,0.0006135119,0.09178054],"category_scores_gemma":[0.001222858,0.0004171519,0.0007104556,0.001384176,0.001701176,0.003477859,0.001783421,0.002445138,0.03957997],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001961704,"about_ca_system_score_gemma":0.001354399,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001077694,"about_ca_topic_score_gemma":0.002063226,"domain_scores_codex":[0.9995327,0.00006081557,0.00002437487,0.0001005283,0.0002267473,0.00005482902],"domain_scores_gemma":[0.9996258,0.0001084103,0.00001901196,0.0000888066,0.0001085541,0.00004937823],"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":[0.00001392004,0.00002317298,0.0001278762,0.0003009317,0.000006690719,0.00008749789,0.0003748854,0.0002804474,0.0007923127,0.7193511,0.1953068,0.08333442],"study_design_scores_gemma":[0.000002144614,0.000006024898,0.0001946178,0.00007872062,0.000002343201,0.0002029566,0.00006322485,0.0001801479,0.0002331521,0.1284271,0.8706054,0.000004174754],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"other","genre_gemma":"methods","genre_scores_codex":[0.001046343,0.004534026,0.01405376,0.001153499,0.0007099782,0.00004996638,0.0005711706,0.0005080154,0.9773731],"genre_scores_gemma":[0.0322485,0.007548107,0.02027637,0.001571329,0.0007632425,0.0001543859,0.002151381,0.0006623831,0.9346243],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.09178054,"threshold_uncertainty_score":0.3070365,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0603350910627213,"score_gpt":0.2604303288080699,"score_spread":0.2000952377453486,"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."}}