{"id":"W4415138678","doi":"10.48550/arxiv.2507.11672","title":"Lower bounds for mask polynomials with many cyclotomic divisors","year":2025,"lang":"en","type":"preprint","venue":"Corvinus Research Archive (Corvinus University of Budapest)","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Nemzeti Kutatási Fejlesztési és Innovációs Hivatal; Natural Sciences and Engineering Research Council of Canada; Magyar Tudományos Akadémia; Hungarian Scientific Research Fund","keywords":"Conjecture; Integer (computer science); Product (mathematics); Simple (philosophy); Set (abstract data type); Polynomial; Cyclotomic polynomial; Range (aeronautics)","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":[0.003144533,0.00254754,0.002281472,0.003914493,0.003321244,0.006276594,0.003461889,0.002042815,0.02144727],"category_scores_gemma":[0.02204527,0.001064851,0.001589363,0.003250128,0.005224624,0.01229886,0.005319129,0.00527898,0.003213115],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004215099,"about_ca_system_score_gemma":0.00153285,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001690431,"about_ca_topic_score_gemma":0.002597589,"domain_scores_codex":[0.9967631,0.0005234188,0.0001147077,0.0007291962,0.0008888039,0.0009808431],"domain_scores_gemma":[0.9799488,0.01502536,0.001146719,0.001510689,0.0008222113,0.001546207],"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":[0.0006962118,0.0001407075,0.003751885,0.0004566658,0.00007811638,0.000275943,0.0005137281,0.0186424,0.004069642,0.9324803,0.01162035,0.02727399],"study_design_scores_gemma":[0.00006214977,0.0001002229,0.001291939,0.0001267652,0.00007495601,0.0003339462,0.000158646,0.07404,0.002748607,0.9137458,0.007255423,0.00006148549],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4766549,0.009954436,0.2994145,0.01172724,0.0008112639,0.0002259366,0.003229976,0.001694743,0.1962869],"genre_scores_gemma":[0.937564,0.002722538,0.0392915,0.0007763953,0.00132788,0.0002841701,0.001637152,0.0004884975,0.01590796],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02144727,"threshold_uncertainty_score":0.07174826,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08821141562103771,"score_gpt":0.3528799386936701,"score_spread":0.2646685230726324,"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."}}