{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7FGMUQSHMMCDRMYF3BR4BOKLCU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"049957a8f8e2860b11ab0c8e3b681fc8ed42b2dc5896a5faf982c5c3e936805a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2009-11-06T19:50:54Z","title_canon_sha256":"f83f4001020b81db709d0cec37d5f7ad9f1225b78b2e6fe7ad7220fa1f441703"},"schema_version":"1.0","source":{"id":"0911.1332","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1332","created_at":"2026-05-18T01:36:07Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1332v3","created_at":"2026-05-18T01:36:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1332","created_at":"2026-05-18T01:36:07Z"},{"alias_kind":"pith_short_12","alias_value":"7FGMUQSHMMCD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7FGMUQSHMMCDRMYF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7FGMUQSH","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:fc29bf7b8c6c0dcc46c4418f4df69e538c7827bb5596c094fa4c8c10d07cb33e","target":"graph","created_at":"2026-05-18T01:36:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The functional equation for Riemann's Zeta function is studied, from which it is shown why all of the non-trivial, full-zeros of the Zeta function $\\zeta (s)$ will only occur on the critical line {$\\sigma=1/2$} where {$s=\\sigma+I \\rho$}, thereby establishing the truth of Riemann's hypothesis. Further, two relatively simple transcendental equations are obtained; the numerical solution of these equations locates all of the zeros of {$\\zeta (s)$} on the critical line.","authors_text":"Michael S. Milgram","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2009-11-06T19:50:54Z","title":"Notes on the Zeros of Riemann's Zeta Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1332","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1201c7198ae7301aac2a242da16feb379516280e67e2eb3e41bd274fad17bd22","target":"record","created_at":"2026-05-18T01:36:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"049957a8f8e2860b11ab0c8e3b681fc8ed42b2dc5896a5faf982c5c3e936805a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2009-11-06T19:50:54Z","title_canon_sha256":"f83f4001020b81db709d0cec37d5f7ad9f1225b78b2e6fe7ad7220fa1f441703"},"schema_version":"1.0","source":{"id":"0911.1332","kind":"arxiv","version":3}},"canonical_sha256":"f94cca4247630438b305d863c0b94b152f4262275c7f4d1800b026a05a936d3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f94cca4247630438b305d863c0b94b152f4262275c7f4d1800b026a05a936d3e","first_computed_at":"2026-05-18T01:36:07.611733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:07.611733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cUR/cX8bdJWliWzGHuDOcRMeLmErEyKa0medV2eKDPyNmZeuN8v+7WciSmMVPXD+KGhrIy6eHKn8OVOXtQl+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:07.612552Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.1332","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1201c7198ae7301aac2a242da16feb379516280e67e2eb3e41bd274fad17bd22","sha256:fc29bf7b8c6c0dcc46c4418f4df69e538c7827bb5596c094fa4c8c10d07cb33e"],"state_sha256":"11842074dcd7c077ac6ecf9c38769c283ec1425d413f0ac46e254a354a737ab7"}