{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XLYF3V6BAVGABDH3HAPLEWLZTB","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":"d12755543d15c65ef9dc7c9b7fedad5969ce6e0b25d462977017d2095e9d844a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T17:05:24Z","title_canon_sha256":"6d259c0a2fce9e325ff297995d2e1dfa721eb202ffc1589bc389511d047f8248"},"schema_version":"1.0","source":{"id":"1808.09927","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09927","created_at":"2026-05-18T00:06:53Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09927v1","created_at":"2026-05-18T00:06:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09927","created_at":"2026-05-18T00:06:53Z"},{"alias_kind":"pith_short_12","alias_value":"XLYF3V6BAVGA","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XLYF3V6BAVGABDH3","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XLYF3V6B","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:e82a1abc3bd8a4edee13b5244e3a3ec5cabf969c3304767bc12906fa56741c7d","target":"graph","created_at":"2026-05-18T00:06:53Z","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 determinant method of Kasteleyn gives a method of computing the number of perfect matchings of a planar bipartite graph. In addition, results of Bernardi exhibit a bijection between spanning trees of a planar bipartite graph and elements of its Jacobian. In this paper, we explore an analogue of Bernardi's results, providing a canonical simply transitive group action of the Kasteleyn cokernel of a planar bipartite graph on its set of perfect matchings, when the planar bipartite graph in question is of the form $G^+$, as defined by Kenyon, Propp and Wilson.","authors_text":"Libby Taylor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T17:05:24Z","title":"Kasteleyn cokernels and perfect matchings on planar bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09927","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:e40382be45b298577f67b7ad6620f4cd463d164f936b4cb6f932d58d8db00f82","target":"record","created_at":"2026-05-18T00:06:53Z","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":"d12755543d15c65ef9dc7c9b7fedad5969ce6e0b25d462977017d2095e9d844a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T17:05:24Z","title_canon_sha256":"6d259c0a2fce9e325ff297995d2e1dfa721eb202ffc1589bc389511d047f8248"},"schema_version":"1.0","source":{"id":"1808.09927","kind":"arxiv","version":1}},"canonical_sha256":"baf05dd7c1054c008cfb381eb25979984b76d83ce9716c08ca53b48c2588be0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baf05dd7c1054c008cfb381eb25979984b76d83ce9716c08ca53b48c2588be0e","first_computed_at":"2026-05-18T00:06:53.957773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:53.957773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p5pC/cArh8si/8piuuNkUC9wjQPcPdTb9cBuL6YOLSDYf72Yl1rFZrWIebcZELjvVoAcvKwoAjYbq+wyN/i6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:53.958427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09927","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e40382be45b298577f67b7ad6620f4cd463d164f936b4cb6f932d58d8db00f82","sha256:e82a1abc3bd8a4edee13b5244e3a3ec5cabf969c3304767bc12906fa56741c7d"],"state_sha256":"2e45adda71107806a1065e6db3cf9a66d350eb0367da20535935247c9630bb0f"}