{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OBMUJH2727UDWR3FPE5YP27BVT","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":"883c97a95f1354f903b6802ef58090c51361e69a9714a825a1cac0a65909ab21","cross_cats_sorted":["math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-28T15:58:46Z","title_canon_sha256":"d8929ecd720d64ca401221147a791baf5821244c314db0a7d3ad0987b63bbe9a"},"schema_version":"1.0","source":{"id":"1101.5559","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5559","created_at":"2026-05-18T02:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5559v3","created_at":"2026-05-18T02:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5559","created_at":"2026-05-18T02:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"OBMUJH2727UD","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OBMUJH2727UDWR3F","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OBMUJH27","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:48394267730326847710ac2c13627c10ff345728d597d061bcbe2ddceaa96693","target":"graph","created_at":"2026-05-18T02:03:20Z","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":"The Kac-Ward formula allows to compute the Ising partition function on any finite graph G from the determinant of 2^{2g} matrices, where g is the genus of a surface in which G embeds. We show that in the case of isoradially embedded graphs with critical weights, these determinants have quite remarkable properties. First of all, they satisfy some generalized Kramers-Wannier duality: there is an explicit equality relating the determinants associated to a graph and to its dual graph. Also, they are proportional to the determinants of the discrete critical Laplacians on the graph G, exactly when t","authors_text":"David Cimasoni","cross_cats":["math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-28T15:58:46Z","title":"The critical Ising model via Kac-Ward matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5559","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":"sha256:3f8681390b44f73049fda4fbbecfe8ef392964f464bfd3a0fb04c538be474563","target":"record","created_at":"2026-05-18T02:03:20Z","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":"883c97a95f1354f903b6802ef58090c51361e69a9714a825a1cac0a65909ab21","cross_cats_sorted":["math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-28T15:58:46Z","title_canon_sha256":"d8929ecd720d64ca401221147a791baf5821244c314db0a7d3ad0987b63bbe9a"},"schema_version":"1.0","source":{"id":"1101.5559","kind":"arxiv","version":3}},"canonical_sha256":"7059449f5fd7e83b4765793b87ebe1ace5d8fb86fb4737744835c9288310ee57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7059449f5fd7e83b4765793b87ebe1ace5d8fb86fb4737744835c9288310ee57","first_computed_at":"2026-05-18T02:03:20.788206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:20.788206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AvaopUfm5EI6V8U60oRgWk7r2e3uLPYh51Yc5aBSUSjBKdtfLdiV9RjCrc0Gg4TpBNNdko85ew3jcDXaKZFSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:20.788641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.5559","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f8681390b44f73049fda4fbbecfe8ef392964f464bfd3a0fb04c538be474563","sha256:48394267730326847710ac2c13627c10ff345728d597d061bcbe2ddceaa96693"],"state_sha256":"696e9e63f118a29984dee3005a75bce9364e4d3d3b6c4a587fab1867d43f066c"}