{"id":"W4396851885","doi":"10.1016/j.aim.2024.109705","title":"Infinitely many commensurability classes of compact Coxeter polyhedra in <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.svg\"><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">H</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:math> and <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si2.svg\"><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">H</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:math>","year":2024,"lang":"lv","type":"article","venue":"Advances in Mathematics","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Canada Research Chairs; University of Toronto","funders":"Agence Nationale de la Recherche","keywords":"Polyhedron; Mathematics; Coxeter group; Commensurability (mathematics); Combinatorics; Discrete mathematics; Pure mathematics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007728092,0.0008227947,0.0008797043,0.001887681,0.004459886,0.006208975,0.001102904,0.001661678,0.02333162],"category_scores_gemma":[0.00383691,0.0007411222,0.001413181,0.001597915,0.003531628,0.004944083,0.003050264,0.003566743,0.002419143],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002149509,"about_ca_system_score_gemma":0.0007191758,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000937329,"about_ca_topic_score_gemma":0.001466681,"domain_scores_codex":[0.9985363,0.0002930473,0.00009279727,0.000349127,0.0004146047,0.0003140483],"domain_scores_gemma":[0.9975287,0.001121912,0.0002541847,0.0004078478,0.0002515132,0.0004357217],"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":[0.0001008662,0.00005511877,0.0004945229,0.00004394976,0.0000163115,0.0002223491,0.0003343419,0.0007006206,0.0009312379,0.9880157,0.002715209,0.006369703],"study_design_scores_gemma":[0.00006579841,0.00006375935,0.001014647,0.00004284994,0.000025038,0.0004549109,0.0005003798,0.005973815,0.001714044,0.9772832,0.01282557,0.00003599086],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5239558,0.0009007726,0.0883271,0.002576501,0.0007239479,0.0001306984,0.0006931914,0.0008261414,0.3818659],"genre_scores_gemma":[0.9515051,0.000370808,0.01139279,0.0003588973,0.0003253773,0.0002064273,0.0009335058,0.0002224268,0.03468467],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02333162,"threshold_uncertainty_score":0.07805204,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02497200623199043,"score_gpt":0.2692032468731882,"score_spread":0.2442312406411978,"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."}}