{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:5AEA3DSE6R4MC3X7UV73JYCDSM","short_pith_number":"pith:5AEA3DSE","schema_version":"1.0","canonical_sha256":"e8080d8e44f478c16effa57fb4e04393393c442961b4ecb2cfb0edc7eb496c67","source":{"kind":"arxiv","id":"1307.8395","version":3},"attestation_state":"computed","paper":{"title":"Statistical and other properties of Riemann zeros based on an explicit equation for the $n$-th zero on the critical line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.NT","authors_text":"Andr\\'e LeClair, Guilherme Fran\\c{c}a","submitted_at":"2013-07-29T20:17:54Z","abstract_excerpt":"We show that there are an infinite number of Riemann zeros on the critical line, enumerated by the positive integers $n=1,2,\\dotsc$, whose ordinates can be obtained as the solution of a new transcendental equation that depends only on $n$. Under weak assumptions, we show that the number of such zeros already saturates the counting formula for the numbers of zeros on the entire critical strip. These results thus constitute a concrete proposal toward verifying the Riemann hypothesis. We perform numerical analyses of the exact equation, and its asymptotic limit of large ordinate. The starting poi"},"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":"1307.8395","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-29T20:17:54Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"3a2b170a86346667c8259197154d7fffcf9d26a87b5698395306f13f7b18c740","abstract_canon_sha256":"ff5db0ac9488e2ad3e574bde0d367212e29b1aeeb34abea3a4c2c5d1d7ee6504"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:44.108020Z","signature_b64":"B/rGE7CcFlk8tGsAw00iQMfDn5NLQuAjftgpKB6iBQn2ebw7tmVYT03b4iXKnWnFHQC2NH2qEFbE53bw7bzMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8080d8e44f478c16effa57fb4e04393393c442961b4ecb2cfb0edc7eb496c67","last_reissued_at":"2026-05-18T02:56:44.107611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:44.107611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Statistical and other properties of Riemann zeros based on an explicit equation for the $n$-th zero on the critical line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.NT","authors_text":"Andr\\'e LeClair, Guilherme Fran\\c{c}a","submitted_at":"2013-07-29T20:17:54Z","abstract_excerpt":"We show that there are an infinite number of Riemann zeros on the critical line, enumerated by the positive integers $n=1,2,\\dotsc$, whose ordinates can be obtained as the solution of a new transcendental equation that depends only on $n$. Under weak assumptions, we show that the number of such zeros already saturates the counting formula for the numbers of zeros on the entire critical strip. These results thus constitute a concrete proposal toward verifying the Riemann hypothesis. We perform numerical analyses of the exact equation, and its asymptotic limit of large ordinate. The starting poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8395","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1307.8395","created_at":"2026-05-18T02:56:44.107677+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.8395v3","created_at":"2026-05-18T02:56:44.107677+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8395","created_at":"2026-05-18T02:56:44.107677+00:00"},{"alias_kind":"pith_short_12","alias_value":"5AEA3DSE6R4M","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"5AEA3DSE6R4MC3X7","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"5AEA3DSE","created_at":"2026-05-18T12:27:34.582898+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/5AEA3DSE6R4MC3X7UV73JYCDSM","json":"https://pith.science/pith/5AEA3DSE6R4MC3X7UV73JYCDSM.json","graph_json":"https://pith.science/api/pith-number/5AEA3DSE6R4MC3X7UV73JYCDSM/graph.json","events_json":"https://pith.science/api/pith-number/5AEA3DSE6R4MC3X7UV73JYCDSM/events.json","paper":"https://pith.science/paper/5AEA3DSE"},"agent_actions":{"view_html":"https://pith.science/pith/5AEA3DSE6R4MC3X7UV73JYCDSM","download_json":"https://pith.science/pith/5AEA3DSE6R4MC3X7UV73JYCDSM.json","view_paper":"https://pith.science/paper/5AEA3DSE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.8395&json=true","fetch_graph":"https://pith.science/api/pith-number/5AEA3DSE6R4MC3X7UV73JYCDSM/graph.json","fetch_events":"https://pith.science/api/pith-number/5AEA3DSE6R4MC3X7UV73JYCDSM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5AEA3DSE6R4MC3X7UV73JYCDSM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5AEA3DSE6R4MC3X7UV73JYCDSM/action/storage_attestation","attest_author":"https://pith.science/pith/5AEA3DSE6R4MC3X7UV73JYCDSM/action/author_attestation","sign_citation":"https://pith.science/pith/5AEA3DSE6R4MC3X7UV73JYCDSM/action/citation_signature","submit_replication":"https://pith.science/pith/5AEA3DSE6R4MC3X7UV73JYCDSM/action/replication_record"}},"created_at":"2026-05-18T02:56:44.107677+00:00","updated_at":"2026-05-18T02:56:44.107677+00:00"}