{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001323896,0.0003948112,0.0003209371,0.001052577,0.001078635,0.001799569,0.0005100909,0.0003500601,0.006865095],"category_scores_gemma":[0.0005350446,0.000264743,0.0004329337,0.0005048143,0.002129243,0.001862688,0.001429684,0.001246966,0.001012655],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005365206,"about_ca_system_score_gemma":0.0002090921,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008727638,"about_ca_topic_score_gemma":0.0009410219,"domain_scores_codex":[0.999662,0.00004371575,0.00001387968,0.0000811299,0.00009336482,0.0001059488],"domain_scores_gemma":[0.999665,0.00005894958,0.00007661925,0.00006138151,0.00005322208,0.00008478658],"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":[0.00005506724,0.00002283883,0.0004365976,0.00002748942,0.000006319456,0.0001873148,0.0003851351,0.001696397,0.007250079,0.9834715,0.0005776319,0.005883521],"study_design_scores_gemma":[0.00005550038,0.0001347899,0.002803179,0.00003348511,0.00002084244,0.0007371939,0.001128812,0.01753065,0.01575991,0.9331158,0.02862529,0.00005461242],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.818037,0.0002037829,0.1062515,0.0002506695,0.00009313594,0.00007703272,0.000354859,0.0002107509,0.0745213],"genre_scores_gemma":[0.9599712,0.0001883666,0.01488815,0.00006543176,0.0001003848,0.00009421508,0.0004376938,0.0001207585,0.02413389],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006865095,"threshold_uncertainty_score":0.02296597,"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."}}