{"id":"W6930974110","doi":"10.5281/zenodo.15567485","title":"Resonance Filtering and Structural Inconsistencies in Weil's Explicit Formula: A Function-Theoretic Prime-Zero Duality Approach","year":2025,"lang":"en","type":"preprint","venue":"Zenodo (CERN European Organization for Nuclear Research)","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Trusted Positioning (Canada)","funders":"","keywords":"Duality (order theory); Riemann hypothesis; Riemann zeta function; Explicit formulae; Dirichlet distribution; Python (programming language); Scaling; Harmonic analysis","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":[0.004011825,0.000567842,0.0007066217,0.002334934,0.001021667,0.002228905,0.001302286,0.001061647,0.004733338],"category_scores_gemma":[0.01610855,0.0003027112,0.000753635,0.0006212217,0.004476331,0.004764305,0.0026644,0.001922322,0.0005631059],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00121127,"about_ca_system_score_gemma":0.000624896,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000383906,"about_ca_topic_score_gemma":0.0002238187,"domain_scores_codex":[0.9986721,0.0004579731,0.00005866149,0.0002073862,0.0004557176,0.0001481228],"domain_scores_gemma":[0.9958221,0.002481777,0.0003925824,0.0006437482,0.0004291874,0.0002306368],"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":[0.00003457823,0.00001834336,0.0006103048,0.00003408659,0.000005338847,0.00007277487,0.0001536785,0.004269425,0.001749202,0.9857867,0.0002808314,0.006984693],"study_design_scores_gemma":[0.00001105331,0.00005352929,0.0004190736,0.0000255938,0.00001042554,0.0001484944,0.0000856238,0.1038484,0.003414784,0.8902008,0.001758814,0.00002344945],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1658413,0.0002792894,0.8120697,0.0007691589,0.0001363066,0.00003749458,0.00006688711,0.0002912583,0.02050872],"genre_scores_gemma":[0.9199578,0.0002015281,0.07464257,0.0002604177,0.0001341092,0.00004674459,0.00005566325,0.0002336013,0.00446742],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004733338,"threshold_uncertainty_score":0.02121681,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07006656091842085,"score_gpt":0.3012360431930802,"score_spread":0.2311694822746593,"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."}}