{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RE57KFD4CVMXR4NUMEBSM2SLAT","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":"53082ab1801712a69e30818c70ea70d79d284cc39ab3e61c8fa6572acbc710c8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T18:12:11Z","title_canon_sha256":"0b172b64fa2d0ef25295d2f6b58cb493a171545670e213207f3649b23b6a566c"},"schema_version":"1.0","source":{"id":"1701.02686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02686","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02686v1","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02686","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"RE57KFD4CVMX","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RE57KFD4CVMXR4NU","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RE57KFD4","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:268c315f930d5bc2a32631907ae106fcb434213f5884c52ba56d579562eb4fb8","target":"graph","created_at":"2026-05-18T00:53:03Z","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":"In this paper, $p$ and $q$ are two different odd primes. First, We construct the congruent elliptic curves corresponding to $p$, $2p$, $pq$, and $2pq,$ then, in the cases of congruent numbers, we determine the rank of the corresponding congruent elliptic curves.","authors_text":"Farzali Izadi, Hamid Reza Abdolmaleki","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T18:12:11Z","title":"On The Rank Of Congruent Elliptic Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02686","kind":"arxiv","version":1},"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:d59eb36d691bde09b4b14d9b56bd1a735c0d06f08f80812b83bbdd5b234c7030","target":"record","created_at":"2026-05-18T00:53:03Z","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":"53082ab1801712a69e30818c70ea70d79d284cc39ab3e61c8fa6572acbc710c8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T18:12:11Z","title_canon_sha256":"0b172b64fa2d0ef25295d2f6b58cb493a171545670e213207f3649b23b6a566c"},"schema_version":"1.0","source":{"id":"1701.02686","kind":"arxiv","version":1}},"canonical_sha256":"893bf5147c155978f1b46103266a4b04ec714ab5a316f84a171b7138d82596fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"893bf5147c155978f1b46103266a4b04ec714ab5a316f84a171b7138d82596fb","first_computed_at":"2026-05-18T00:53:03.659272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:03.659272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v6Six6/Z/xfD1580k7YmTHTl+U7A7AMFsvdODzzDOgW0t593KM2A95MtcJ56H6+pqeLKqSfenCLJNVimzWTIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:03.659948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d59eb36d691bde09b4b14d9b56bd1a735c0d06f08f80812b83bbdd5b234c7030","sha256:268c315f930d5bc2a32631907ae106fcb434213f5884c52ba56d579562eb4fb8"],"state_sha256":"55caa1a3fa2f55c157b5dbfa1b75e40bf3381b74463c663f89d03d3c533f762d"}