{"id":"W2900444034","doi":"10.1145/3431922","title":"Uniform, Integral, and Feasible Proofs for the Determinant Identities","year":2021,"lang":"en","type":"article","venue":"Journal of the ACM","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"National Natural Science Foundation of China","keywords":"Mathematical proof; Mathematics; Axiom; Bounded function; Discrete mathematics; Polynomial; Class (philosophy); Proof complexity; Algebra over a field; Pure mathematics; Computer science","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":[0.000418105,0.0000565234,0.0001012916,0.00003238141,0.0002576001,0.0002629449,0.002114569,0.00001758927,0.000003971973],"category_scores_gemma":[0.00055856,0.00002654857,0.0001390066,0.0001672055,0.00007291853,0.0003063582,0.001002954,0.0001502679,4.932785e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001396025,"about_ca_system_score_gemma":0.0000945076,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003080802,"about_ca_topic_score_gemma":0.00001851174,"domain_scores_codex":[0.9994312,0.00003752252,0.0001761082,0.00006957292,0.0001748563,0.0001107176],"domain_scores_gemma":[0.9987018,0.0002884033,0.0001573714,0.0006579488,0.0001657415,0.00002871931],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00009128705,0.000364184,0.005799604,0.0002387755,0.0004893479,0.0002037401,0.006867467,0.000230268,0.003813523,0.2804457,0.08966103,0.6117951],"study_design_scores_gemma":[0.0005727462,0.0001810929,0.01047614,0.0001816176,0.00005363383,0.002338205,0.0005751125,0.0126837,0.01381407,0.9251754,0.03381696,0.0001313133],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3962287,0.01202246,0.4626605,0.1193179,0.008488669,0.0005932155,0.00001241726,0.00004212325,0.0006339923],"genre_scores_gemma":[0.6953726,0.001064587,0.2964652,0.002025827,0.0007759925,0.00001214868,2.305365e-7,0.00001668408,0.004266709],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6447297,"threshold_uncertainty_score":0.3929431,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03872084732340131,"score_gpt":0.2797191853381604,"score_spread":0.2409983380147591,"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."}}