{"id":"W2107854391","doi":"10.1287/moor.25.4.539.12117","title":"A Further Extension of the KKMS Theorem","year":2000,"lang":"en","type":"article","venue":"Mathematics of Operations Research","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Intersection (aeronautics); Generalization; Extension (predicate logic); Countable set; Intersection theorem; Point (geometry); Property (philosophy); Fixed-point theorem; Discrete mathematics; Combinatorics; Brouwer fixed-point theorem; Danskin's theorem; Computer science; Mathematical analysis; Geometry","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":[0.001708266,0.0006117512,0.0007889565,0.001628323,0.001733469,0.002321462,0.001376754,0.0008967355,0.02235696],"category_scores_gemma":[0.005613938,0.0003760587,0.001536681,0.001409464,0.002725759,0.009128358,0.006758372,0.002892107,0.002869106],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001436203,"about_ca_system_score_gemma":0.0009963214,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001090774,"about_ca_topic_score_gemma":0.0008007082,"domain_scores_codex":[0.9980798,0.0003560248,0.0001126593,0.0006770488,0.0005650042,0.0002094763],"domain_scores_gemma":[0.9980218,0.0005885066,0.0001913454,0.0005301411,0.0004998424,0.000168415],"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":[0.00001734717,0.00001977209,0.0003286379,0.00004297718,0.00001046494,0.00005900739,0.0002455144,0.0005897674,0.0006874856,0.9852766,0.002466468,0.01025593],"study_design_scores_gemma":[0.00002121571,0.00005231534,0.001085904,0.00002942601,0.00001850534,0.0003529496,0.000217481,0.004276803,0.0009743584,0.9413127,0.05163179,0.00002650348],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.07755987,0.001368134,0.4364321,0.008154753,0.0007911968,0.0002365007,0.001359184,0.0004723528,0.4736258],"genre_scores_gemma":[0.8318915,0.001361927,0.08806711,0.002580303,0.001354482,0.0003856353,0.001060823,0.0001989081,0.07309934],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02235696,"threshold_uncertainty_score":0.07479149,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1299904349143645,"score_gpt":0.439962566356688,"score_spread":0.3099721314423235,"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."}}