{"id":"W7103753776","doi":"10.1016/j.jnt.2025.10.005","title":"Scattering constants for some families of noncongruence subgroups","year":2025,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Kronecker delta; Limit (mathematics); Scattering; Constant (computer programming); Scattering theory","routes":{"ca_aff":true,"ca_fund":true,"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":[0.002485908,0.00124283,0.0008395516,0.004832317,0.003372007,0.005182856,0.002188263,0.002054388,0.01164667],"category_scores_gemma":[0.009286359,0.0009355156,0.001400789,0.002443474,0.003956698,0.006867224,0.002923989,0.003504746,0.0009213603],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002991182,"about_ca_system_score_gemma":0.0009391896,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001291853,"about_ca_topic_score_gemma":0.0008825298,"domain_scores_codex":[0.9989223,0.000282047,0.00007103659,0.0001983765,0.0002825394,0.0002435902],"domain_scores_gemma":[0.9933124,0.004412353,0.0005621735,0.0004445463,0.0004702214,0.0007981758],"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":[0.00006260915,0.0000297243,0.0007110299,0.00002759261,0.00001267788,0.0001201454,0.0005738119,0.0005212931,0.001039656,0.9943193,0.0007258205,0.001856274],"study_design_scores_gemma":[0.0000436218,0.00002199668,0.0007451971,0.00002499625,0.00002256972,0.0003807814,0.0003806498,0.010853,0.001641945,0.983995,0.001860819,0.00002947368],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8133516,0.001116645,0.08315583,0.002904991,0.0002395041,0.0001065148,0.0002777391,0.0003672222,0.09847999],"genre_scores_gemma":[0.9778064,0.0004014829,0.00768751,0.0002464697,0.0001466876,0.0000834219,0.0002801559,0.0001076523,0.0132402],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01164667,"threshold_uncertainty_score":0.03896195,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03966313918063025,"score_gpt":0.369530739919175,"score_spread":0.3298676007385447,"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."}}