{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7JHX6BBRODXTAQCANQLFIDGSM5","short_pith_number":"pith:7JHX6BBR","schema_version":"1.0","canonical_sha256":"fa4f7f043170ef3040406c16540cd2675f15fe365c71c7aafe8dc00870b2075f","source":{"kind":"arxiv","id":"2607.04316","version":1},"attestation_state":"computed","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-"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.04316","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-05T14:07:00Z","cross_cats_sorted":[],"title_canon_sha256":"74a7f56457e4683983f3dc9e9794e5e6c83181db74cb568bfc1c4fa7593efd41","abstract_canon_sha256":"b9d482156e715a1c47e6f7699b3a4f1878b43badfe0ffc063eb3ff2499c8c920"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:19:08.474778Z","signature_b64":"6P2AfkRanbj8xVmhtlK/ec4LDh10gZigUi2yhKOUDjj2OT9p8iihoV2ZLI6SI/heo//5aTQm9uvhV1J3mSDwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa4f7f043170ef3040406c16540cd2675f15fe365c71c7aafe8dc00870b2075f","last_reissued_at":"2026-07-07T02:19:08.473988Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:19:08.473988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.04316","created_at":"2026-07-07T02:19:08.474129+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.04316v1","created_at":"2026-07-07T02:19:08.474129+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04316","created_at":"2026-07-07T02:19:08.474129+00:00"},{"alias_kind":"pith_short_12","alias_value":"7JHX6BBRODXT","created_at":"2026-07-07T02:19:08.474129+00:00"},{"alias_kind":"pith_short_16","alias_value":"7JHX6BBRODXTAQCA","created_at":"2026-07-07T02:19:08.474129+00:00"},{"alias_kind":"pith_short_8","alias_value":"7JHX6BBR","created_at":"2026-07-07T02:19:08.474129+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7JHX6BBRODXTAQCANQLFIDGSM5","json":"https://pith.science/pith/7JHX6BBRODXTAQCANQLFIDGSM5.json","graph_json":"https://pith.science/api/pith-number/7JHX6BBRODXTAQCANQLFIDGSM5/graph.json","events_json":"https://pith.science/api/pith-number/7JHX6BBRODXTAQCANQLFIDGSM5/events.json","paper":"https://pith.science/paper/7JHX6BBR"},"agent_actions":{"view_html":"https://pith.science/pith/7JHX6BBRODXTAQCANQLFIDGSM5","download_json":"https://pith.science/pith/7JHX6BBRODXTAQCANQLFIDGSM5.json","view_paper":"https://pith.science/paper/7JHX6BBR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.04316&json=true","fetch_graph":"https://pith.science/api/pith-number/7JHX6BBRODXTAQCANQLFIDGSM5/graph.json","fetch_events":"https://pith.science/api/pith-number/7JHX6BBRODXTAQCANQLFIDGSM5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7JHX6BBRODXTAQCANQLFIDGSM5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7JHX6BBRODXTAQCANQLFIDGSM5/action/storage_attestation","attest_author":"https://pith.science/pith/7JHX6BBRODXTAQCANQLFIDGSM5/action/author_attestation","sign_citation":"https://pith.science/pith/7JHX6BBRODXTAQCANQLFIDGSM5/action/citation_signature","submit_replication":"https://pith.science/pith/7JHX6BBRODXTAQCANQLFIDGSM5/action/replication_record"}},"created_at":"2026-07-07T02:19:08.474129+00:00","updated_at":"2026-07-07T02:19:08.474129+00:00"}