{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:JOY7LT2TBA3LD33UBZNIAS36ID","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":"71959b25b96769dc88f5e566de255f46837c3c669c7c2cece6675f4b2d7d7dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-02-29T12:36:45Z","title_canon_sha256":"6dfd9b1d9645231c236f969ca0eb52fb924cc084702bfd8bcc88270ec6645605"},"schema_version":"1.0","source":{"id":"0802.4377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.4377","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"arxiv_version","alias_value":"0802.4377v1","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.4377","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"pith_short_12","alias_value":"JOY7LT2TBA3L","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JOY7LT2TBA3LD33U","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JOY7LT2T","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:36051030fb78f5d8b159c12cef587fe44ffe9a7038d387ce9d6d029211ef0177","target":"graph","created_at":"2026-05-18T01:27:08Z","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":"We shall show that 9, 165 are all of the odd unitary super perfect numbers.","authors_text":"Tomohiro Yamada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-02-29T12:36:45Z","title":"Unitary super perfect numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.4377","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:c8eb87f1231d53e81ffd0e1ca9cfb5dc25a7062f32c599fba8722088ca63611f","target":"record","created_at":"2026-05-18T01:27:08Z","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":"71959b25b96769dc88f5e566de255f46837c3c669c7c2cece6675f4b2d7d7dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-02-29T12:36:45Z","title_canon_sha256":"6dfd9b1d9645231c236f969ca0eb52fb924cc084702bfd8bcc88270ec6645605"},"schema_version":"1.0","source":{"id":"0802.4377","kind":"arxiv","version":1}},"canonical_sha256":"4bb1f5cf530836b1ef740e5a804b7e40ccec1b3527090a2f650488699ada3fb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bb1f5cf530836b1ef740e5a804b7e40ccec1b3527090a2f650488699ada3fb9","first_computed_at":"2026-05-18T01:27:08.461760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:08.461760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0QMFUqkolmNXexbu73cGWnHYQ61joF649prA0qshMnz6AamvBON2Qr45JKwWW8bEahkOjFiWUCPmugMIt4anBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:08.462517Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.4377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8eb87f1231d53e81ffd0e1ca9cfb5dc25a7062f32c599fba8722088ca63611f","sha256:36051030fb78f5d8b159c12cef587fe44ffe9a7038d387ce9d6d029211ef0177"],"state_sha256":"b068e76c743399efeb2ab84b9c0e4a026eec4fe4b11f9a24419177a98fdbcc10"}