{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:D3KEEIZQFZ5U7TQ34HMLPPCVEX","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":"8d5e0e7f3e451b3d45bc934e204f307454964d3f0986455cad073e060a4dbc40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-12T20:35:18Z","title_canon_sha256":"065a37c04398e5a7dae304a3809ca92197b5e0c3031ee54357a9be13896f40f0"},"schema_version":"1.0","source":{"id":"1112.2688","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2688","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2688v3","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2688","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"D3KEEIZQFZ5U","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D3KEEIZQFZ5U7TQ3","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D3KEEIZQ","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:70410d2636993bce89d9b244ba995aaefb38e37f4af9a10cfca3f45b70ce5dd4","target":"graph","created_at":"2026-05-18T01:26:03Z","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":"This article lists all the solution of the Catalan equation $x^p-y^q=1$ for $x,y \\in \\mathbb{Z}[i]$, when one of the primes $p and q$ is even.","authors_text":"Prem Prakash Pandey, R. Balasubramanian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-12T20:35:18Z","title":"Catalan's Equation For Even Primes over Quadratic Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2688","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":"sha256:7e0e968c0007f010a03dfe24360ecdcfd17241a299fb095ba52ef47220581df1","target":"record","created_at":"2026-05-18T01:26:03Z","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":"8d5e0e7f3e451b3d45bc934e204f307454964d3f0986455cad073e060a4dbc40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-12T20:35:18Z","title_canon_sha256":"065a37c04398e5a7dae304a3809ca92197b5e0c3031ee54357a9be13896f40f0"},"schema_version":"1.0","source":{"id":"1112.2688","kind":"arxiv","version":3}},"canonical_sha256":"1ed44223302e7b4fce1be1d8b7bc5525f75dc4886c4eab2d7b8227621028b218","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ed44223302e7b4fce1be1d8b7bc5525f75dc4886c4eab2d7b8227621028b218","first_computed_at":"2026-05-18T01:26:03.283959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:03.283959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sMnvV0WoGC1A978MjDx7EqJEOZEHu2KxJGh804aPG0znsNmdvqg+t7vOKOOT7TS7UiJNa2p0UTT020hfmu5/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:03.284616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2688","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e0e968c0007f010a03dfe24360ecdcfd17241a299fb095ba52ef47220581df1","sha256:70410d2636993bce89d9b244ba995aaefb38e37f4af9a10cfca3f45b70ce5dd4"],"state_sha256":"628eaac22f77554291c83dc8a3e3b70254dd3ffc580841a54f7bb2f2082e73df"}