{"id":"W4416243120","doi":"10.48550/arxiv.2508.08003","title":"Counting Salem numbers arising from arithmetic hyperbolic orbifolds","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Centers for Disease Control and Prevention; Banff International Research Station for Mathematical Innovation and Discovery","keywords":"Dimension (graph theory); Generalization; Polynomial; Commensurability (mathematics); Upper and lower bounds; Exponent; Integer (computer science); Degree (music); Number theory","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":[0.001288387,0.0004997593,0.0006482058,0.003342043,0.001296505,0.002042516,0.001263952,0.0007529975,0.003847729],"category_scores_gemma":[0.007179431,0.0003612658,0.0004397819,0.001328032,0.00397819,0.00475431,0.001733053,0.001127269,0.0002566675],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001159925,"about_ca_system_score_gemma":0.0003985002,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005214871,"about_ca_topic_score_gemma":0.000563363,"domain_scores_codex":[0.9991767,0.0001508621,0.00004397834,0.000180263,0.0003347207,0.0001135457],"domain_scores_gemma":[0.9975628,0.001216586,0.0004447387,0.0002463976,0.0002290693,0.0003004858],"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":[0.00008653424,0.00001322871,0.003519013,0.0000763151,0.00001036837,0.0002041922,0.0002772782,0.002687994,0.006052251,0.9800792,0.0005913604,0.006402194],"study_design_scores_gemma":[0.00001861878,0.000039167,0.003005227,0.00003325334,0.00001492091,0.0007106557,0.0002468984,0.04837495,0.006215972,0.9391681,0.002136531,0.000035647],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8991082,0.0006228423,0.08288365,0.0006647239,0.0001010881,0.00003182729,0.0001874567,0.0001213124,0.01627885],"genre_scores_gemma":[0.9853344,0.0003237473,0.01110291,0.00006018174,0.000166237,0.00005130161,0.0001713065,0.00004270374,0.00274721],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003847729,"threshold_uncertainty_score":0.01287192,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07990046507747883,"score_gpt":0.3302665703755991,"score_spread":0.2503661052981203,"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."}}