{"paper":{"title":"A Gaussian-Perron Smoothed Prime-Side Defect for Local Profiles Near Critical-Line Zeros of the Riemann Zeta Function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Netzer Moriya","submitted_at":"2026-07-05T14:07:00Z","abstract_excerpt":"We introduce a Gaussian--Perron prime-force defect that compares a smoothed prime-side logarithmic force with the logarithmic derivative of the Riemann zeta function. The construction turns the explicit formula into a local diagnostic for zero geometry. Its kernel produces an error-function prime weight and an anisotropic zero-side damping law, with an explicit boundary separating amplified and suppressed nonlocal zero contributions. We prove an exact zero-side formula, derive a universal selected-zero profile on the logarithmic scale, and formulate a finite-window damping certificate for non-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04316","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.04316/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}