{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZL7RIABO5CYSOEPDXIW7XEEQUE","short_pith_number":"pith:ZL7RIABO","schema_version":"1.0","canonical_sha256":"caff14002ee8b12711e3ba2dfb9090a13dfa345f5fb1e4b9b147c5e08bf96a0f","source":{"kind":"arxiv","id":"1708.05266","version":2},"attestation_state":"computed","paper":{"title":"An explicit Gross-Zagier formula related to the Sylvester Conjecture","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hongbo Yin, Jie Shu, Yueke Hu","submitted_at":"2017-08-17T13:48:53Z","abstract_excerpt":"Let $p\\equiv 4,7\\mod 9$ be a rational prime number such that $3\\mod p$ is not a cubic residue. In this paper we prove the 3-part of the product of the full BSD conjectures for $E_p$ and $E_{3p^3}$ is true using an explicit Gross-Zagier formula, where $E_p: x^3+y^3=p$ and $E_{3p^2}: x^3+y^3=3p^2$ are the elliptic curves related to the Sylvester conjecture and cube sum problems."},"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":"1708.05266","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2017-08-17T13:48:53Z","cross_cats_sorted":[],"title_canon_sha256":"0376f75e3d45749556ffe6ba7845b90c294e0109f943e0b68c1c6a5f43cc2255","abstract_canon_sha256":"e2479ecd450a9f973b684d832482ab48db74082710b664a87de15009cdbe439a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:41.721520Z","signature_b64":"DflXSpgRehxH84k/rfZhfLWViusKZiCeH24zi2uBPEwg5SvBnt/Uc+0gy0goW3wTlOq5hcGInzOcW8xhIeARDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caff14002ee8b12711e3ba2dfb9090a13dfa345f5fb1e4b9b147c5e08bf96a0f","last_reissued_at":"2026-05-18T00:03:41.720892Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:41.720892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An explicit Gross-Zagier formula related to the Sylvester Conjecture","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hongbo Yin, Jie Shu, Yueke Hu","submitted_at":"2017-08-17T13:48:53Z","abstract_excerpt":"Let $p\\equiv 4,7\\mod 9$ be a rational prime number such that $3\\mod p$ is not a cubic residue. In this paper we prove the 3-part of the product of the full BSD conjectures for $E_p$ and $E_{3p^3}$ is true using an explicit Gross-Zagier formula, where $E_p: x^3+y^3=p$ and $E_{3p^2}: x^3+y^3=3p^2$ are the elliptic curves related to the Sylvester conjecture and cube sum problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05266","kind":"arxiv","version":2},"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":"1708.05266","created_at":"2026-05-18T00:03:41.720981+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.05266v2","created_at":"2026-05-18T00:03:41.720981+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05266","created_at":"2026-05-18T00:03:41.720981+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZL7RIABO5CYS","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZL7RIABO5CYSOEPD","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZL7RIABO","created_at":"2026-05-18T12:31:59.375834+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/ZL7RIABO5CYSOEPDXIW7XEEQUE","json":"https://pith.science/pith/ZL7RIABO5CYSOEPDXIW7XEEQUE.json","graph_json":"https://pith.science/api/pith-number/ZL7RIABO5CYSOEPDXIW7XEEQUE/graph.json","events_json":"https://pith.science/api/pith-number/ZL7RIABO5CYSOEPDXIW7XEEQUE/events.json","paper":"https://pith.science/paper/ZL7RIABO"},"agent_actions":{"view_html":"https://pith.science/pith/ZL7RIABO5CYSOEPDXIW7XEEQUE","download_json":"https://pith.science/pith/ZL7RIABO5CYSOEPDXIW7XEEQUE.json","view_paper":"https://pith.science/paper/ZL7RIABO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.05266&json=true","fetch_graph":"https://pith.science/api/pith-number/ZL7RIABO5CYSOEPDXIW7XEEQUE/graph.json","fetch_events":"https://pith.science/api/pith-number/ZL7RIABO5CYSOEPDXIW7XEEQUE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZL7RIABO5CYSOEPDXIW7XEEQUE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZL7RIABO5CYSOEPDXIW7XEEQUE/action/storage_attestation","attest_author":"https://pith.science/pith/ZL7RIABO5CYSOEPDXIW7XEEQUE/action/author_attestation","sign_citation":"https://pith.science/pith/ZL7RIABO5CYSOEPDXIW7XEEQUE/action/citation_signature","submit_replication":"https://pith.science/pith/ZL7RIABO5CYSOEPDXIW7XEEQUE/action/replication_record"}},"created_at":"2026-05-18T00:03:41.720981+00:00","updated_at":"2026-05-18T00:03:41.720981+00:00"}