{"id":"W2950736391","doi":"10.48550/arxiv.0908.4460","title":"The Ma-Trudinger-Wang curvature for natural mechanical actions","year":2009,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Curvature; Anharmonicity; Hamiltonian (control theory); Action (physics); Mathematics; Quartic function; Harmonic oscillator; Mathematical analysis; Mathematical physics; Physics; Pure mathematics; Geometry; Quantum mechanics; Mathematical optimization","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0006297548,0.0004124574,0.0005516658,0.0002591447,0.0006704922,0.0001819897,0.001011119,0.0006098931,0.00005275734],"category_scores_gemma":[0.0006775545,0.0003243644,0.0009140593,0.0009751323,0.00007482039,0.0001361094,0.0004571638,0.001406794,0.00002471964],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002451198,"about_ca_system_score_gemma":0.0001198286,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001767538,"about_ca_topic_score_gemma":0.0001853311,"domain_scores_codex":[0.9980813,0.0001296123,0.0003166934,0.0008045746,0.000163372,0.0005044994],"domain_scores_gemma":[0.996993,0.001006383,0.0004303864,0.001068757,0.0003582136,0.0001432581],"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":[0.0001274689,0.0001736196,0.00006634909,0.0001144331,0.0008751053,0.0000387774,0.0000718778,0.00209453,0.00004469302,0.9582106,0.036228,0.00195449],"study_design_scores_gemma":[0.0006535046,0.00006980392,0.0002157928,0.0001127532,0.00165435,0.000006392318,0.0004781962,0.05307607,0.00008833653,0.8911948,0.05173603,0.0007139464],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3374448,0.003134495,0.6291317,0.004717826,0.006723364,0.003944566,0.000249524,0.001115756,0.01353795],"genre_scores_gemma":[0.9842474,0.0003489818,0.002180885,0.0001053616,0.0004019763,0.000004580656,0.00005263503,0.00003681476,0.01262129],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6468027,"threshold_uncertainty_score":0.9999208,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1441935564930597,"score_gpt":0.245932770992679,"score_spread":0.1017392144996193,"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."}}