{"id":"W1981474194","doi":"10.1007/pl00000136","title":"A functional equation generated by event commutativity in separable and additive utility theory","year":2001,"lang":"en","type":"article","venue":"Aequationes Mathematicae","topic":"Functional Equations Stability Results","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Separable space; Order (exchange); Differentiable function; Commutative property; Event (particle physics); Combinatorics; Function (biology); Pure mathematics; Mathematical analysis; Physics","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":[0.001885949,0.0006500643,0.0009156984,0.001043322,0.001630897,0.002424549,0.001166213,0.001606486,0.006978059],"category_scores_gemma":[0.003599448,0.0004601738,0.001288935,0.001290368,0.003002571,0.006348197,0.002131601,0.002538584,0.0004682042],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001823292,"about_ca_system_score_gemma":0.001222388,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002485977,"about_ca_topic_score_gemma":0.001477916,"domain_scores_codex":[0.9993491,0.0002210978,0.00004247293,0.0001398623,0.0001549838,0.00009249273],"domain_scores_gemma":[0.9986601,0.0006940262,0.000149868,0.0001182899,0.0002434879,0.000134212],"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":[0.000004330383,0.000004188521,0.00003461946,0.000005422604,0.000003152515,0.00002077062,0.00005071237,0.000541223,0.00008975171,0.9985618,0.0001793613,0.0005047835],"study_design_scores_gemma":[0.000005939322,0.000003368045,0.00003781322,0.000002162817,0.000003756799,0.00002662899,0.00001959366,0.00669717,0.00006242765,0.9925956,0.0005420271,0.000003691127],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2262596,0.001367086,0.6845485,0.006429106,0.0004283365,0.00006120968,0.0004245055,0.0001637264,0.0803179],"genre_scores_gemma":[0.9283811,0.0007965518,0.03755741,0.0004899566,0.0003803825,0.00009463621,0.0002081779,0.00007863692,0.0320132],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006978059,"threshold_uncertainty_score":0.02334398,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07981121703752203,"score_gpt":0.3175378349053706,"score_spread":0.2377266178678485,"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."}}