{"id":"W4383709622","doi":"10.48550/arxiv.2307.04393","title":"Transport-entropy forms of direct and Converseblaschke-Santal{\\\\'o}\\n inequalities","year":2023,"lang":"en","type":"preprint","venue":"HAL (Le Centre pour la Communication Scientifique Directe)","topic":"Material Science and Thermodynamics","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Azrieli Foundation; Centre National de la Recherche Scientifique; Fondation Simone et Cino Del Duca","keywords":"Inequality; Mathematics; Entropy (arrow of time); Mathematical economics; Econometrics; Thermodynamics; Physics; Mathematical analysis","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":[0.002018391,0.0002632997,0.000407931,0.0001491667,0.00009839877,0.0001016146,0.0005532901,0.0002101171,0.0001150051],"category_scores_gemma":[0.0001440504,0.0002626684,0.0001231408,0.0002077099,0.0002390303,0.0001289415,0.0003230553,0.000249856,0.00001266148],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005169644,"about_ca_system_score_gemma":0.0000601064,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008813399,"about_ca_topic_score_gemma":0.00125432,"domain_scores_codex":[0.9981358,0.0004573035,0.0004665057,0.0003693982,0.0002808215,0.0002901468],"domain_scores_gemma":[0.9981979,0.0003603287,0.0001757399,0.0008256796,0.0003225881,0.0001177906],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.00006962562,0.00050361,0.01264483,0.006018973,0.0007253533,0.00003616391,0.0641891,0.006292521,0.1040416,0.777247,0.000605999,0.02762527],"study_design_scores_gemma":[0.002163918,0.000003230894,0.03174282,0.007978016,0.0002973254,0.00001900926,0.002132126,0.3681722,0.4749019,0.097782,0.01194291,0.002864598],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9340731,0.0003962579,0.01686953,0.0004131229,0.0004488787,0.0003301844,0.0003318783,0.0005335384,0.04660354],"genre_scores_gemma":[0.9950446,0.001780817,0.001451519,0.000009688795,0.00001366546,0.00003435057,0.0003094102,0.0000507309,0.001305158],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.679465,"threshold_uncertainty_score":0.9999825,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01400324549786927,"score_gpt":0.207144180594892,"score_spread":0.1931409350970227,"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."}}