{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3F5UMEJULNX3MSRE6TSREINPZF","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":"9907e31c2408d4521d7e6fd43c36f8dac115c076666f5e4ed76648b0b010e9de","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2015-01-23T14:01:08Z","title_canon_sha256":"ee83a88797b8795dee3ce9c5cc70850658f6346263e28f7804da06601189fa1f"},"schema_version":"1.0","source":{"id":"1501.05803","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05803","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05803v1","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05803","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"pith_short_12","alias_value":"3F5UMEJULNX3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3F5UMEJULNX3MSRE","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3F5UMEJU","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:f0a701767f8d6a2bda96ec1d9a534f215584f13128e243633db607824fb4ebf2","target":"graph","created_at":"2026-05-18T02:28:48Z","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, the theory of elliptic curves is used for finding the solutions of the quartic Diophantine equation $X^4+Y^4=2(U^4+V^4)$\n  Keywords: Diophantine equation, Elliptic curve, Congruent number","authors_text":"Farzali Izadi, Kamran Nabardi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2015-01-23T14:01:08Z","title":"Diophantine Equation $X^4+Y^4=2(U^4+V^4)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05803","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":"sha256:7f561495af0eda26b02bf8fe6ca8963c47f9915540ec4d73817fc54383603bb1","target":"record","created_at":"2026-05-18T02:28:48Z","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":"9907e31c2408d4521d7e6fd43c36f8dac115c076666f5e4ed76648b0b010e9de","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2015-01-23T14:01:08Z","title_canon_sha256":"ee83a88797b8795dee3ce9c5cc70850658f6346263e28f7804da06601189fa1f"},"schema_version":"1.0","source":{"id":"1501.05803","kind":"arxiv","version":1}},"canonical_sha256":"d97b4611345b6fb64a24f4e51221afc950f737ea4de71c7fe2bdad780b63c760","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d97b4611345b6fb64a24f4e51221afc950f737ea4de71c7fe2bdad780b63c760","first_computed_at":"2026-05-18T02:28:48.936782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:48.936782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o4MRC1Epubb4J3XJzpKqE3eDqP95tV3vITNAlyrp1uxFJfoA7TY6wPcuAaGblAwFc1eGIhRsciKXgjdl8gNAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:48.937169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05803","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f561495af0eda26b02bf8fe6ca8963c47f9915540ec4d73817fc54383603bb1","sha256:f0a701767f8d6a2bda96ec1d9a534f215584f13128e243633db607824fb4ebf2"],"state_sha256":"6681db1351091cc4a8e9e012e4f773c041097af75055049a60a6ee7cf23bd691"}