{"id":"W2724268121","doi":"10.5486/pmd.2004.3062","title":"On a composite functional equation arising in utility theory","year":2004,"lang":"en","type":"article","venue":"Publicationes Mathematicae Debrecen","topic":"Functional Equations Stability Results","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Hungarian Scientific Research Fund","keywords":"Mathematics; Composite number; Functional equation; Calculus (dental); Algebra over a field; Applied mathematics; Mathematical economics; Pure mathematics; Mathematical analysis; Algorithm; Differential equation; Medicine; Orthodontics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.002131064,0.0002650149,0.0003366565,0.0004169476,0.0002204617,0.0001283756,0.0002789896,0.0001444363,0.0006405266],"category_scores_gemma":[0.007239128,0.0002464742,0.0001175038,0.0009063171,0.0001232627,0.000515022,0.00006809783,0.0002858849,0.0005265834],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004717049,"about_ca_system_score_gemma":0.000192971,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002001208,"about_ca_topic_score_gemma":0.00004267134,"domain_scores_codex":[0.9972896,0.0002285381,0.0008816602,0.0005270244,0.0007263561,0.0003468012],"domain_scores_gemma":[0.9951331,0.003261746,0.0002965247,0.0008113575,0.0003808813,0.0001164047],"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":[0.0001403138,0.001318596,0.0003355524,0.0001039749,0.00003157429,6.00571e-7,0.0007881629,0.0004820326,0.0002008858,0.9945148,0.000341487,0.001741982],"study_design_scores_gemma":[0.001142818,0.00003767575,0.015295,0.0001050517,0.00002445591,0.00001441894,0.0001587532,0.004194411,0.0004181831,0.9782428,0.0001356701,0.0002307265],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4016837,0.00003603676,0.5556479,0.009489451,0.0002418246,0.001466095,0.00004116388,0.0004912699,0.03090256],"genre_scores_gemma":[0.9726276,0.000002369427,0.02617267,0.0003057488,0.0000668456,0.0003437542,0.0001496541,0.00004167225,0.0002897027],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5709438,"threshold_uncertainty_score":0.9999987,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1030635087959562,"score_gpt":0.3119197638966551,"score_spread":0.2088562551006989,"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."}}