{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006226657,0.0007991776,0.0005052206,0.001440149,0.0008951733,0.002756056,0.0007793364,0.001183085,0.006696308],"category_scores_gemma":[0.001220789,0.0002286239,0.000539079,0.0007326133,0.002243263,0.00342157,0.001316911,0.002042485,0.001134041],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008162557,"about_ca_system_score_gemma":0.0004487466,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004698714,"about_ca_topic_score_gemma":0.0004133185,"domain_scores_codex":[0.9996186,0.00007931817,0.0000175033,0.00008783121,0.0001257186,0.00007093948],"domain_scores_gemma":[0.9995984,0.00005529579,0.00006640927,0.00008664226,0.0001077206,0.00008553646],"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":[0.000004947582,0.000008837632,0.00006328466,0.000008209799,0.00000191145,0.00004811107,0.00007821487,0.0002281554,0.001027111,0.9961605,0.000532735,0.001837938],"study_design_scores_gemma":[0.00001169161,0.00005022004,0.000287755,0.00002358464,0.000007241316,0.0005793152,0.0001991991,0.009531444,0.00180015,0.960808,0.02667806,0.00002341555],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2351363,0.0022212,0.4035665,0.005098754,0.002723271,0.0001282206,0.0003751584,0.0006049563,0.3501456],"genre_scores_gemma":[0.8864135,0.001526719,0.06174096,0.002152186,0.001085126,0.000131283,0.0001920675,0.0002736135,0.04648453],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006696308,"threshold_uncertainty_score":0.02240139,"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."}}