{"id":"W4318242410","doi":"10.48550/arxiv.2301.10627","title":"MV polytopes and reduced double Bruhat cells","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Bijection; Polytope; Combinatorics; Vertex (graph theory); Mathematics; Bruhat order; Weyl group; Bounded function; Algebraic number; Graph","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":[0.0001537068,0.0003594833,0.0004724711,0.0001647733,0.0001553644,0.00009263027,0.0005522747,0.0004374744,0.0000714865],"category_scores_gemma":[0.00002878237,0.0003869127,0.0001855327,0.00023554,0.000112907,0.000101714,0.001311335,0.0005204281,0.00004944112],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001083161,"about_ca_system_score_gemma":0.000108524,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003426834,"about_ca_topic_score_gemma":0.00004943392,"domain_scores_codex":[0.9984273,0.0000602147,0.0002133729,0.0008496069,0.0001019521,0.0003475765],"domain_scores_gemma":[0.9985291,0.000183674,0.0002225787,0.0008068091,0.00008585815,0.0001719313],"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":[0.0001173867,0.00004088249,0.0001836051,0.0002259156,0.000180066,0.0001282603,0.000320034,0.001808314,0.0001937924,0.9948233,0.001920413,0.00005805686],"study_design_scores_gemma":[0.0008745018,0.00003714056,0.0001690901,0.0001077601,0.0001936544,0.000002598306,0.0001852859,0.001820483,0.001189181,0.9947777,0.0001995113,0.0004430276],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.993845,0.00006335577,0.001440176,0.00008778853,0.001972748,0.0004069078,0.00001801825,0.0003249537,0.001841019],"genre_scores_gemma":[0.9885658,0.0002549662,0.0002014327,0.00002635866,0.000210977,0.000001404599,0.000009221683,0.0000625523,0.01066729],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008826268,"threshold_uncertainty_score":0.9998583,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1582834712643359,"score_gpt":0.2284128295641134,"score_spread":0.07012935829977743,"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."}}