{"id":"W2135224290","doi":"","title":"A Representation Theorem for Domains with Discrete and Continuous Variables","year":2001,"lang":"en","type":"article","venue":"Érudit documents and data repository (Érudit Consortium, University of Montreal)","topic":"Computability, Logic, AI Algorithms","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"Social Sciences and Humanities Research Council of Canada","keywords":"Representation theorem; Mathematics; Representation (politics); Generalization; Axiom; Brouwer fixed-point theorem; Order (exchange); Fundamental theorem; Discrete mathematics; Danskin's theorem; Pure mathematics; Algebra over a field; Fixed-point theorem; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0003554246,0.0002328456,0.0004198974,0.000104567,0.0004947868,0.0001701959,0.0009425538,0.0000834571,0.000005605802],"category_scores_gemma":[0.00006497604,0.0002143042,0.0000493412,0.0002156987,0.0004004813,0.001273328,0.001006174,0.00009366246,4.91573e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009126179,"about_ca_system_score_gemma":0.00006270684,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004305218,"about_ca_topic_score_gemma":0.002148497,"domain_scores_codex":[0.9979661,0.0001439747,0.0002833397,0.0009985404,0.00030183,0.0003062618],"domain_scores_gemma":[0.9974517,0.0004823302,0.0003497107,0.001352286,0.000181187,0.0001827365],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"not_applicable","study_design_scores_codex":[0.005334133,0.002216158,0.3137474,0.0008316508,0.003429093,0.004912561,0.004465156,0.0008309088,0.003797019,0.1651077,0.0370576,0.4582707],"study_design_scores_gemma":[0.04164755,0.005781907,0.2896776,0.0009797792,0.00276234,0.005482265,0.00680011,0.1962918,0.001858048,0.05792052,0.3856911,0.00510695],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3308938,0.001010089,0.6576976,0.001647729,0.0003812392,0.001555848,0.0003152568,0.0002410854,0.006257338],"genre_scores_gemma":[0.9489474,0.0008676721,0.04817237,0.00005173124,0.00009674405,0.000003949941,0.0001442926,0.00001674525,0.001699102],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6180536,"threshold_uncertainty_score":0.8739073,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0120707649566475,"score_gpt":0.2299994266069857,"score_spread":0.2179286616503382,"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."}}