{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4KDDRX6POCE6PYITICIYWGQ37U","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":"d16cdde94ee69cd7fc580cf86373a4a30c42acf1ea6f543c5613a92d715e7324","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-12T03:46:00Z","title_canon_sha256":"4841506860af94441a534142c08a35c57c17532b4a6225b78a795c2c8c2d1c4c"},"schema_version":"1.0","source":{"id":"1310.3332","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3332","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3332v4","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3332","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"4KDDRX6POCE6","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4KDDRX6POCE6PYIT","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4KDDRX6P","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:c1343440177b4fe8e3dcd47cacde19cc250148fbbde961e3e49f0181c609887d","target":"graph","created_at":"2026-05-18T02:43:24Z","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 use the subgraph replacement method to prove a simple product formula for the tilings of an 8-vertex counterpart of Propp's quasi-hexagons (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999), called quasi-octagon.","authors_text":"Tri Lai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-12T03:46:00Z","title":"Enumeration of Hybrid Domino-Lozenge Tilings II: Quasi-octagonal regions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3332","kind":"arxiv","version":4},"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":"sha256:149ae1a1d8c2a7d119be86e867c90953ddcf8e647ac190095d8079910891bd50","target":"record","created_at":"2026-05-18T02:43:24Z","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":"d16cdde94ee69cd7fc580cf86373a4a30c42acf1ea6f543c5613a92d715e7324","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-12T03:46:00Z","title_canon_sha256":"4841506860af94441a534142c08a35c57c17532b4a6225b78a795c2c8c2d1c4c"},"schema_version":"1.0","source":{"id":"1310.3332","kind":"arxiv","version":4}},"canonical_sha256":"e28638dfcf7089e7e11340918b1a1bfd22dcbcbf187c8048f74058b1883934bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e28638dfcf7089e7e11340918b1a1bfd22dcbcbf187c8048f74058b1883934bb","first_computed_at":"2026-05-18T02:43:24.261341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:24.261341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3aFKu7u6ZQ3wcGNgnYCI9zjEEDazVWHrCVyCoWoHPXE0kNv6DzJyOTSIPrJyMCUc6EPtr3Kl3OdWocKMcgDXAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:24.261742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3332","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:149ae1a1d8c2a7d119be86e867c90953ddcf8e647ac190095d8079910891bd50","sha256:c1343440177b4fe8e3dcd47cacde19cc250148fbbde961e3e49f0181c609887d"],"state_sha256":"d7c6a6945dade4e3dcdb071e2bf504738b8370a99218c1e2f5fd0132bdae3c97"}