{"id":"W4361806747","doi":"10.48550/arxiv.2303.16569","title":"Shi arrangements and low elements in Coxeter groups","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Coxeter group; Mathematics; Combinatorics; Hyperplane; Conjecture; Coxeter element; Weyl group; Artin group; Affine transformation; Coxeter complex; Type (biology); Pure mathematics","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":[0.0003749696,0.000384181,0.0005407876,0.000315384,0.00006981128,0.00004595233,0.0005506295,0.0002941695,0.00005048866],"category_scores_gemma":[0.0002568417,0.0004600312,0.0001120258,0.0003616827,0.00008566538,0.0001568975,0.001506629,0.0005785422,0.00009145318],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002919254,"about_ca_system_score_gemma":0.00004629043,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002305797,"about_ca_topic_score_gemma":0.00009242575,"domain_scores_codex":[0.9981626,0.00008001074,0.0004073847,0.0007923676,0.0001407716,0.0004169238],"domain_scores_gemma":[0.9982837,0.0003438907,0.000353216,0.0008152726,0.00007604948,0.0001278438],"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":[0.0001587921,0.0008271097,0.0240267,0.003200144,0.0004352667,0.001281052,0.001691194,0.003008234,0.00008377746,0.9635705,0.001421032,0.0002962226],"study_design_scores_gemma":[0.001331424,0.00003618917,0.0006375909,0.0004949793,0.0001017045,0.000001066526,0.0002679902,0.01156457,0.00004079417,0.9850258,0.00006263955,0.0004352241],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9830257,0.00001453119,0.01368265,0.00003319988,0.0009148221,0.0008291229,0.0000330072,0.0002468052,0.001220146],"genre_scores_gemma":[0.9953749,0.0001303252,0.001899456,0.00002480036,0.00007326162,0.000006253764,0.00001762792,0.00008280035,0.002390547],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02338911,"threshold_uncertainty_score":0.9997851,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1613900437178745,"score_gpt":0.2460022861305314,"score_spread":0.08461224241265691,"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."}}