{"id":"W7149875408","doi":"","title":"Orientation of alcoves in affine Weyl groups","year":2025,"lang":"en","type":"preprint","venue":"HAL (Le Centre pour la Communication Scientifique Directe)","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; Centre National de la Recherche Scientifique","keywords":"Weyl group; Affine transformation; Variety (cybernetics); Bijection; Intersection (aeronautics); Irreducible representation; Orientation (vector space); Group (periodic table)","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":[0.0003103243,0.0004236557,0.0003300907,0.001375218,0.001071995,0.002202937,0.0003683949,0.0004570941,0.002441104],"category_scores_gemma":[0.0006463585,0.0002309931,0.0004101543,0.0007914527,0.003364453,0.002272887,0.001493572,0.0009009689,0.0004352421],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007449157,"about_ca_system_score_gemma":0.0002910522,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008680372,"about_ca_topic_score_gemma":0.0007184631,"domain_scores_codex":[0.9995346,0.00005786362,0.00001963451,0.00007092398,0.0001263214,0.0001906049],"domain_scores_gemma":[0.9996035,0.00006053766,0.0001053562,0.00004116597,0.00005098768,0.0001385586],"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":[0.00004021788,0.00002458751,0.0009391831,0.00002283797,0.00000487231,0.0001525216,0.000776579,0.0007501712,0.003843676,0.9863703,0.0003434653,0.006731568],"study_design_scores_gemma":[0.00002636989,0.00007654498,0.002171657,0.00002267826,0.00001336806,0.00039177,0.0008830365,0.002817612,0.003364078,0.981078,0.009121221,0.00003367454],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9192544,0.0005729554,0.02812761,0.0003220975,0.00009807384,0.00003894862,0.0001162014,0.0001062184,0.0513636],"genre_scores_gemma":[0.988667,0.0003172462,0.00365431,0.00005766611,0.00009939847,0.00002421151,0.00008762344,0.00003307058,0.007059595],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002441104,"threshold_uncertainty_score":0.008166313,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02281442524620469,"score_gpt":0.2877040924037239,"score_spread":0.2648896671575192,"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."}}