{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2YOAQGZF674QPRPDDBMPUW65RS","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":"9b469cd096c508a1a14488d68bac88a73bd24f5240b4c5ccb96bb389722ec972","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-29T19:12:20Z","title_canon_sha256":"e4fab6f0664abd5c047045a1f0a7fa2341f1b302f66342cb7590d976a661e52c"},"schema_version":"1.0","source":{"id":"1602.09106","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.09106","created_at":"2026-05-18T01:19:51Z"},{"alias_kind":"arxiv_version","alias_value":"1602.09106v1","created_at":"2026-05-18T01:19:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.09106","created_at":"2026-05-18T01:19:51Z"},{"alias_kind":"pith_short_12","alias_value":"2YOAQGZF674Q","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2YOAQGZF674QPRPD","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2YOAQGZF","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:271620e651146375907ac48beca49ba1a5db4c7fffdfbc537b0ee6d525625b07","target":"graph","created_at":"2026-05-18T01:19:51Z","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":"One of the many number theoretic topics investigated by the ancient Greeks was perfect numbers, which are positive integers equal to the sum of their proper positive integral divisors. Mathematicians from Euclid to Euler investigated these mysterious numbers. We present results on perfect numbers in the ring of Eisenstein integers.","authors_text":"Jeff Rushall, Jordan Hunt, Zachary Parker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-29T19:12:20Z","title":"Perfect Numbers in the Ring of Eisenstein Integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.09106","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":"sha256:32cec2dc39fce1981972f32d1ca34a542d89d047d741ff0f858b225250e61073","target":"record","created_at":"2026-05-18T01:19:51Z","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":"9b469cd096c508a1a14488d68bac88a73bd24f5240b4c5ccb96bb389722ec972","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-29T19:12:20Z","title_canon_sha256":"e4fab6f0664abd5c047045a1f0a7fa2341f1b302f66342cb7590d976a661e52c"},"schema_version":"1.0","source":{"id":"1602.09106","kind":"arxiv","version":1}},"canonical_sha256":"d61c081b25f7f907c5e31858fa5bdd8c9390270e50699f4a866a2b2cd8a8173f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d61c081b25f7f907c5e31858fa5bdd8c9390270e50699f4a866a2b2cd8a8173f","first_computed_at":"2026-05-18T01:19:51.285034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:51.285034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kNM9XbUd9Oo8D4MolKmIVgeHyRkdqo2QLbcXNUJrzRB15e/ovWxBmodcubdcnL5/McTUOv0Nc4bALjDPLJJLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:51.285672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.09106","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32cec2dc39fce1981972f32d1ca34a542d89d047d741ff0f858b225250e61073","sha256:271620e651146375907ac48beca49ba1a5db4c7fffdfbc537b0ee6d525625b07"],"state_sha256":"4da7bc967f02cfc869d9917f6cb1f7d66dcca1ed6f493d04a532096ab52488af"}