{"id":"W2951881394","doi":"10.48550/arxiv.math-ph/0212022","title":"Duality, monotonicity and the Wigner-Yanase-Dyson metrics","year":2002,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"","keywords":"Metric (unit); Mathematics; Monotone polygon; Monotonic function; Scalar (mathematics); Pure mathematics; Duality (order theory); Mathematical physics; Combinatorics; 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":[0.001479891,0.0006175145,0.0005812365,0.001776705,0.00105956,0.002020963,0.0007444878,0.0008832671,0.002336859],"category_scores_gemma":[0.004699552,0.0003215208,0.0004403617,0.0008186619,0.002468875,0.003276659,0.00222724,0.00133231,0.0005279414],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008183242,"about_ca_system_score_gemma":0.0004754381,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004634137,"about_ca_topic_score_gemma":0.0003468716,"domain_scores_codex":[0.9990336,0.0003790184,0.00004522198,0.0001161856,0.0003031817,0.0001227645],"domain_scores_gemma":[0.9982381,0.0005708538,0.0003455971,0.000150836,0.0004072649,0.0002874512],"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":[0.000007972584,0.000007676034,0.0002142435,0.00001065349,0.000002160022,0.00004423892,0.00006192937,0.0006848184,0.0008556468,0.9961129,0.0004523799,0.001545221],"study_design_scores_gemma":[0.000005326992,0.0000216131,0.0005147331,0.00001395766,0.000003874482,0.0002970062,0.0000634738,0.0211915,0.001127418,0.9738801,0.002867164,0.0000139555],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.549753,0.002495122,0.2975999,0.002792907,0.0002539083,0.00007162338,0.0002737669,0.0001385906,0.1466213],"genre_scores_gemma":[0.9577596,0.001137495,0.0315064,0.0002882685,0.0002252832,0.0001010943,0.0001524999,0.00007512423,0.008754304],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002336859,"threshold_uncertainty_score":0.007826507,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1494646408468379,"score_gpt":0.3491610733316531,"score_spread":0.1996964324848153,"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."}}