{"id":"W1977405062","doi":"10.1007/s00153-003-0205-z","title":"Matrix identities and the pigeonhole principle","year":2004,"lang":"en","type":"article","venue":"Archive for Mathematical Logic","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto; McMaster University","funders":"","keywords":"Pigeonhole principle; Mathematical proof; Mathematics; Bounded function; Matrix (chemical analysis); Algebra over a field; Discrete mathematics; Pure mathematics; Calculus (dental); Mathematical analysis","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":[],"consensus_categories":[],"category_scores_codex":[0.0003290017,0.00006898143,0.0001064248,0.00003944433,0.0001808323,0.000116978,0.0002457544,0.00001497442,0.000006725004],"category_scores_gemma":[0.0001829924,0.00004155275,0.00005971773,0.00008819613,0.0001236137,0.0001349788,0.0001505896,0.00004602178,0.00004066389],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000008290408,"about_ca_system_score_gemma":0.00002399067,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001113911,"about_ca_topic_score_gemma":0.000001293558,"domain_scores_codex":[0.9994062,0.000028555,0.0001541174,0.0001519238,0.0001297726,0.0001293915],"domain_scores_gemma":[0.9992053,0.0005237085,0.00004118036,0.0001617389,0.0000293622,0.00003869085],"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":[0.000007605072,0.00002502077,0.000001372735,0.0000263853,0.000006801399,7.865316e-7,0.000422955,0.001073043,0.00007183831,0.9977427,0.00004716259,0.0005743428],"study_design_scores_gemma":[0.0007071772,0.00005073543,0.0001390594,0.000009156813,0.000006299827,0.00002973001,0.00001488144,0.03534194,0.0002333054,0.962867,0.0005437029,0.00005706439],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01116929,0.00009747954,0.9839668,0.002255168,0.00005856585,0.0003208152,0.000004031348,0.00004641656,0.002081381],"genre_scores_gemma":[0.5813611,0.00001220494,0.4172597,0.0004777217,0.00007388512,0.0001056667,0.000007515797,0.000005039049,0.0006971402],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.5701919,"threshold_uncertainty_score":0.1694472,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01728469457103503,"score_gpt":0.2881806004346795,"score_spread":0.2708959058636444,"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."}}