{"id":"W4387560906","doi":"10.48550/arxiv.2310.06267","title":"A Pair of Garside Shadows","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Narodowe Centrum Nauki; National Science Foundation","keywords":"Conjecture; Cone (formal languages); Type (biology); Combinatorics; Mathematics; Algorithm; Geology","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":[0.0002888512,0.0004735804,0.0007629014,0.0008647215,0.001295366,0.001555423,0.0003932418,0.0005077934,0.01089887],"category_scores_gemma":[0.001426805,0.0004186839,0.0006194288,0.0006974452,0.001860558,0.002415288,0.002030434,0.001280675,0.001320859],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003375769,"about_ca_system_score_gemma":0.0002580389,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003235555,"about_ca_topic_score_gemma":0.0003468372,"domain_scores_codex":[0.9995455,0.00003979334,0.00001730392,0.0001334754,0.0001328972,0.0001310326],"domain_scores_gemma":[0.9990497,0.000261558,0.00007684607,0.0002533802,0.0001374086,0.0002210265],"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":[0.000469933,0.00005227666,0.004296996,0.0001114131,0.00002588142,0.001259752,0.001414026,0.001567016,0.03639321,0.9140955,0.002379264,0.03793464],"study_design_scores_gemma":[0.00005562493,0.0003589352,0.006621935,0.00008252604,0.00005288507,0.002404816,0.001540662,0.01166065,0.0367002,0.899313,0.04114928,0.00005950027],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7265628,0.0004820785,0.1588517,0.0003364903,0.000321087,0.00005934863,0.0003081926,0.0006606907,0.1124176],"genre_scores_gemma":[0.9553813,0.0001858851,0.02596101,0.0001698356,0.00006588336,0.00002878637,0.0002623821,0.0002034284,0.01774157],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01089887,"threshold_uncertainty_score":0.03646034,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.165466924097855,"score_gpt":0.227664861198105,"score_spread":0.06219793710025001,"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."}}