{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003042401,0.0001524551,0.0005648219,0.0002204436,0.00007513871,0.00002745366,0.000523321,0.0000710065,0.0006860688],"category_scores_gemma":[0.002095599,0.0001245778,0.0002835919,0.000230218,0.0003996867,0.000261472,0.0001096964,0.0002628473,0.00001373202],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009963826,"about_ca_system_score_gemma":0.0002719472,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003485685,"about_ca_topic_score_gemma":0.000003414151,"domain_scores_codex":[0.9981588,0.0002216472,0.0008374045,0.0001320441,0.0003593623,0.0002908079],"domain_scores_gemma":[0.993963,0.004614977,0.0005389957,0.0003116775,0.000487237,0.00008413815],"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":[0.0008023111,0.0002312685,0.003412572,0.0006629978,0.0005567095,0.00003555056,0.0005840774,0.00000458771,0.00565265,0.9709864,0.01157904,0.00549185],"study_design_scores_gemma":[0.0009994186,0.00006850713,0.0002355687,0.000653518,0.0001319808,0.0001021219,0.002099426,0.00004623027,0.009183844,0.9846442,0.001719398,0.0001157533],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9389288,0.0003015243,0.03611767,0.0004550222,0.0005882411,0.0004066933,0.000112063,0.00002554613,0.02306447],"genre_scores_gemma":[0.9847648,0.00005925469,0.01031784,0.0001545805,0.0001373118,0.000008485783,0.000001034305,0.00002767776,0.00452904],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04583601,"threshold_uncertainty_score":0.7511973,"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."}}