{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:KFEKKBUZV7WWURXXLIZUEZCI5A","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":"573f4d86233eef5c601fc9a2f1f9455b14cf5b6eb2c40a899e79f2a95477908c","cross_cats_sorted":["math.GT","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-08-31T17:02:59Z","title_canon_sha256":"b118553a7f38915071d46204b62e35586a502649dbafe1209104e0dabfba8777"},"schema_version":"1.0","source":{"id":"math-ph/0608070","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0608070","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0608070v2","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0608070","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"KFEKKBUZV7WW","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"KFEKKBUZV7WWURXX","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"KFEKKBUZ","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:8b4100e23cd8d54b5fb6a1f2271c088a17fde7f150e7650dcf23a4dd28d5ef39","target":"graph","created_at":"2026-05-18T01:38:32Z","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":"Partition functions for dimers on closed oriented surfaces are known to be alternating sums of Pfaffians of Kasteleyn matrices. In this paper, we obtain the formula for the coefficients in terms of discrete spin structures.","authors_text":"David Cimasoni, Nicolai Reshetikhin","cross_cats":["math.GT","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-08-31T17:02:59Z","title":"Dimers on surface graphs and spin structures. I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0608070","kind":"arxiv","version":2},"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":"sha256:4a7949293c9260eb6e24d566f02233998b06e7b6abd22eb2eef53e510b4fc5b4","target":"record","created_at":"2026-05-18T01:38:32Z","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":"573f4d86233eef5c601fc9a2f1f9455b14cf5b6eb2c40a899e79f2a95477908c","cross_cats_sorted":["math.GT","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-08-31T17:02:59Z","title_canon_sha256":"b118553a7f38915071d46204b62e35586a502649dbafe1209104e0dabfba8777"},"schema_version":"1.0","source":{"id":"math-ph/0608070","kind":"arxiv","version":2}},"canonical_sha256":"5148a50699afed6a46f75a33426448e81b266bad3f5c543287bd816002d1e7fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5148a50699afed6a46f75a33426448e81b266bad3f5c543287bd816002d1e7fd","first_computed_at":"2026-05-18T01:38:32.660242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:32.660242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+CfGc0ruQYqozTIy1Mbri6wMxj7TD/Yb7ISP5xs+Ny44BKkGNzYrSxfMmsz2GLcLmTmnfJSUA4ZDvZrL6QJ1Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:32.660989Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0608070","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a7949293c9260eb6e24d566f02233998b06e7b6abd22eb2eef53e510b4fc5b4","sha256:8b4100e23cd8d54b5fb6a1f2271c088a17fde7f150e7650dcf23a4dd28d5ef39"],"state_sha256":"cf903b533f212dd7af4d9dafbbc719d81b076fecec7c1e1ac3a82356074d3c46"}