{"id":"W2126396674","doi":"10.1007/s12044-013-0139-2","title":"A short note on sign changes","year":2013,"lang":"en","type":"article","venue":"Proceedings - Mathematical Sciences","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Sign (mathematics); Mathematics; Congruence subgroup; Congruence (geometry); Modular group; Combinatorics; Fourier series; Modular form; Pure mathematics; Mathematical analysis; Geometry","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":[0.002513222,0.001210369,0.001049993,0.001570167,0.003672272,0.003957401,0.002731669,0.002730772,0.03336739],"category_scores_gemma":[0.01907637,0.0003920563,0.001287884,0.002010013,0.004840257,0.01063576,0.003675209,0.009471172,0.01646895],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001031147,"about_ca_system_score_gemma":0.0009860552,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008139765,"about_ca_topic_score_gemma":0.0008981071,"domain_scores_codex":[0.997861,0.0004328202,0.0002088115,0.0004237894,0.0008488201,0.0002248289],"domain_scores_gemma":[0.9903123,0.004619103,0.0004903479,0.00214736,0.002010119,0.0004206818],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0002859289,0.0000492322,0.0002729754,0.0003148877,0.00002564139,0.0007819247,0.0003084069,0.0003332271,0.004650914,0.5924622,0.3161313,0.08438336],"study_design_scores_gemma":[0.00002683376,0.00006019785,0.0004927705,0.0001447977,0.00002967039,0.0006942282,0.0001507666,0.0005591881,0.004021851,0.4959432,0.4978076,0.00006878108],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"editorial","genre_gemma":"empirical","genre_scores_codex":[0.008617286,0.01730958,0.1526289,0.1222202,0.396978,0.0001217082,0.001193244,0.002338046,0.298593],"genre_scores_gemma":[0.2134753,0.02505703,0.1068335,0.06021747,0.1190267,0.0005110496,0.001567639,0.007806037,0.4655052],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.03336739,"threshold_uncertainty_score":0.1116251,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1262163816316292,"score_gpt":0.3893629149074407,"score_spread":0.2631465332758115,"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."}}