{"id":"W2139863157","doi":"10.1090/s0025-5718-2015-02925-1","title":"Conditional bounds for the least quadratic non-residue and related problems","year":2015,"lang":"en","type":"preprint","venue":"Mathematics of Computation","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada; Simons Foundation; National Science Foundation","keywords":"Mathematics; Quadratic residue; Quadratic equation; Riemann hypothesis; Residue (chemistry); Class number; Upper and lower bounds; Applied mathematics; Discrete mathematics; Pure mathematics; Mathematical analysis","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":[0.002641444,0.0002976563,0.0006559059,0.0001612835,0.00015754,0.0001382362,0.0003884617,0.0002573953,0.00003796323],"category_scores_gemma":[0.001139396,0.0002243913,0.0001640956,0.0001388929,0.000357967,0.00007583968,0.0003774232,0.0004271081,0.00001503421],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009828539,"about_ca_system_score_gemma":0.00033259,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001537153,"about_ca_topic_score_gemma":0.00001302724,"domain_scores_codex":[0.9976435,0.0001116349,0.0009701133,0.0003136293,0.0007135284,0.0002476519],"domain_scores_gemma":[0.9939677,0.003712674,0.0008908715,0.0004689129,0.0008703991,0.00008946803],"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":[0.00007514331,0.001087347,0.00008543547,0.02289383,0.001975189,0.000004508076,0.02514688,0.04979859,0.0001820242,0.8728613,0.02450778,0.00138196],"study_design_scores_gemma":[0.0004315811,0.00005445887,0.0000351703,0.0003631427,0.0002072197,0.00001540213,0.0005220182,0.3797867,0.00003887117,0.6183972,0.00001406871,0.0001341469],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08055359,0.0002686785,0.9113806,0.0008383428,0.0002224397,0.003490808,0.000155114,0.00008480468,0.003005649],"genre_scores_gemma":[0.9350901,0.00001358916,0.06267529,0.00001253181,0.00009143261,0.0002926073,0.0002307088,0.00008712551,0.001506627],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8545365,"threshold_uncertainty_score":0.9150413,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.101732865647481,"score_gpt":0.3808835953054122,"score_spread":0.2791507296579311,"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."}}