{"id":"W2951246964","doi":"10.48550/arxiv.1005.2162","title":"On the local structure of optimal measures in the multi-marginal optimal transportation problem","year":2010,"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":"Natural Sciences and Engineering Research Council of Canada","keywords":"Dimension (graph theory); Mathematical optimization; Transportation theory; Order (exchange); Mathematics; Function (biology); Marginal cost; Computer science; Economics; Combinatorics; Microeconomics","routes":{"ca_aff":true,"ca_fund":true,"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":[],"consensus_categories":[],"category_scores_codex":[0.0006029604,0.0003254487,0.0004456403,0.000298239,0.000108716,0.00004075855,0.001014662,0.0004246091,0.0001450078],"category_scores_gemma":[0.0001186787,0.0002041314,0.0003408197,0.0008652611,0.0002034685,0.00007559476,0.00006961333,0.001693743,0.000004373658],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005964154,"about_ca_system_score_gemma":0.0001061988,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001908337,"about_ca_topic_score_gemma":0.00139482,"domain_scores_codex":[0.9983846,0.0002316207,0.0003390749,0.0005183011,0.0002692693,0.0002571529],"domain_scores_gemma":[0.9981122,0.0004661908,0.0004123807,0.0007668999,0.0001920338,0.00005029163],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0001791298,0.000385959,0.001569205,0.0001681822,0.0002629209,0.00007535809,0.0021876,0.7310645,0.0001312849,0.263362,0.0003011506,0.0003127233],"study_design_scores_gemma":[0.004768701,0.0005835173,0.04891823,0.0008272966,0.00375313,0.00001591967,0.01503939,0.6096576,0.001683061,0.3110941,0.00127567,0.002383435],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8545803,0.00002117035,0.1444461,0.0001081054,0.00007557091,0.0004625879,0.00006664763,0.000019732,0.0002197672],"genre_scores_gemma":[0.9966437,0.00002021754,0.003047846,0.00003722513,0.00003678015,0.000001697896,0.00004322698,0.00002019517,0.000149155],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1420633,"threshold_uncertainty_score":0.8324238,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07810135610943518,"score_gpt":0.2123943983551313,"score_spread":0.1342930422456961,"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."}}