{"id":"W2517549071","doi":"10.48550/arxiv.1608.05541","title":"Complex Legendre duality","year":2016,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Legendre transformation; Legendre polynomials; Homogeneous space; Duality (order theory); Metric (unit); Mathematics; Pure mathematics; Manifold (fluid mechanics); Space (punctuation); Property (philosophy); Mathematical analysis; Computer science; Geometry; Philosophy; Epistemology; Economics","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","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0003482314,0.0004260687,0.0005650967,0.0002148289,0.00018514,0.00005121155,0.001041847,0.0003973252,0.001868],"category_scores_gemma":[0.00009249596,0.0004203882,0.0003849062,0.0003039322,0.0001540576,0.0001213932,0.001620364,0.0004928858,0.0004748314],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001866596,"about_ca_system_score_gemma":0.0001082513,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005348765,"about_ca_topic_score_gemma":0.00005637767,"domain_scores_codex":[0.9979338,0.0002297895,0.000299983,0.0009491334,0.0001252759,0.0004620191],"domain_scores_gemma":[0.9974862,0.0003013172,0.0003410126,0.001494656,0.0001776881,0.0001991575],"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":[0.0000496442,0.000181325,0.00191074,0.0003300772,0.0001712028,0.0002369214,0.00009068995,0.0003469781,0.00008126195,0.9874823,0.009025796,0.00009305285],"study_design_scores_gemma":[0.0005898813,0.00003683682,0.002547998,0.00009855021,0.0001926032,0.0000095863,0.0001412448,0.001889266,0.000118041,0.9869133,0.00682411,0.0006386355],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7274076,0.00003423276,0.1661717,0.0003107,0.0008046774,0.0005932645,0.0002943026,0.0006494793,0.103734],"genre_scores_gemma":[0.9833859,0.0000199237,0.0006422102,0.0000747683,0.0002147798,0.000001019591,0.00003196512,0.00004045207,0.015589],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2559783,"threshold_uncertainty_score":0.9998248,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2908834424919098,"score_gpt":0.2478096618868151,"score_spread":0.04307378060509473,"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."}}