{"id":"W2952587785","doi":"10.48550/arxiv.1008.4419","title":"Optimal transportation, topology and uniqueness","year":2010,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Uniqueness; Countable set; Mathematics; Sequence (biology); Manifold (fluid mechanics); Function (biology); Graph; Topology (electrical circuits); Domain (mathematical analysis); Transportation theory; Discrete mathematics; Mathematical optimization; Combinatorics; Mathematical analysis","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":[0.0002330574,0.0002572022,0.0004525279,0.0002962876,0.0001024483,0.00003608155,0.0003481971,0.0006257409,0.0002937262],"category_scores_gemma":[0.00007160519,0.0002699329,0.0001836277,0.0004443383,0.0001521793,0.00008875162,0.0001153235,0.0007928252,0.000009640019],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003381424,"about_ca_system_score_gemma":0.00008154431,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001696661,"about_ca_topic_score_gemma":0.0005834023,"domain_scores_codex":[0.9988161,0.00006846635,0.0002125495,0.0006167488,0.00006221818,0.0002238971],"domain_scores_gemma":[0.9987613,0.0001618833,0.0002278565,0.0005385986,0.0001827093,0.0001276461],"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":[0.00007014258,0.0002241677,0.01321809,0.0003489992,0.0005082323,0.0003379527,0.0006871076,0.01921014,0.00008538554,0.963929,0.0009854331,0.0003953339],"study_design_scores_gemma":[0.001705921,0.0001325312,0.02102518,0.0001306271,0.002782668,0.00001795169,0.001538847,0.04282917,0.0004263006,0.9201981,0.007418091,0.001794616],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9203116,0.00005780188,0.07807375,0.00007940637,0.0002154643,0.0001598608,0.00003067097,0.00007926534,0.0009921738],"genre_scores_gemma":[0.9947355,0.0001620952,0.002719798,0.00003554745,0.00006941959,9.07096e-7,0.00005628441,0.00002169966,0.002198719],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07535395,"threshold_uncertainty_score":0.9999753,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06881849044092193,"score_gpt":0.2137538657666771,"score_spread":0.1449353753257552,"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."}}