{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7PRG4O5NGR2533V4ZLWV2YFXXY","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":"a3fe31cc44d7977dca2816542a51465bdc7be6cecd489fb2a374c24234c8dab5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-20T19:19:42Z","title_canon_sha256":"117ecfe3e50710d69cb4c35171d19d3f3151847b2045f132226691d64a400469"},"schema_version":"1.0","source":{"id":"1105.4158","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4158","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4158v2","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4158","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"7PRG4O5NGR25","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7PRG4O5NGR2533V4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7PRG4O5N","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:d31b95e97523702e6982b3baa11071bf136011b8977753077be4e9c5a42a5884","target":"graph","created_at":"2026-05-18T02:21:50Z","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 dimer model is the study of random dimer covers (perfect matchings) of a graph. A double-dimer configuration on a graph $G$ is a union of two dimer covers of $G$. We introduce quaternion weights in the dimer model and show how they can be used to study the homotopy classes (relative to a fixed set of faces) of loops in the double dimer model on a planar graph. As an application we prove that, in the scaling limit of the \"uniform\" double-dimer model on ${\\mathbb Z}^2$ (or on any other bipartite planar graph conformally approximating $\\mathbb C$), the loops are conformally invariant.\n  As ot","authors_text":"Richard Kenyon","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-20T19:19:42Z","title":"Conformal invariance of loops in the double-dimer model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4158","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":"sha256:0da792b7d0f0ace46aaa6653bdc090f05751979e71da24fb74289fcf5963599c","target":"record","created_at":"2026-05-18T02:21:50Z","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":"a3fe31cc44d7977dca2816542a51465bdc7be6cecd489fb2a374c24234c8dab5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-20T19:19:42Z","title_canon_sha256":"117ecfe3e50710d69cb4c35171d19d3f3151847b2045f132226691d64a400469"},"schema_version":"1.0","source":{"id":"1105.4158","kind":"arxiv","version":2}},"canonical_sha256":"fbe26e3bad3475ddeebccaed5d60b7be26b85386cb5a87755810edd577bc279e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbe26e3bad3475ddeebccaed5d60b7be26b85386cb5a87755810edd577bc279e","first_computed_at":"2026-05-18T02:21:50.329457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:50.329457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VXo9aBR2GTT61p4WbtSy7t33QjT8leoTOWX2c/IbevjQM1AGJUrgHU3bOMSnfHn/6Q5IhZT8w0E64dd/BEMsDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:50.329921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4158","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0da792b7d0f0ace46aaa6653bdc090f05751979e71da24fb74289fcf5963599c","sha256:d31b95e97523702e6982b3baa11071bf136011b8977753077be4e9c5a42a5884"],"state_sha256":"1b2a01bd3150294f56e05c19501f18eeb60868cbacfc16d23f7a587288366459"}