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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1105.4158","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-20T19:19:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"117ecfe3e50710d69cb4c35171d19d3f3151847b2045f132226691d64a400469","abstract_canon_sha256":"a3fe31cc44d7977dca2816542a51465bdc7be6cecd489fb2a374c24234c8dab5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:50.329921Z","signature_b64":"VXo9aBR2GTT61p4WbtSy7t33QjT8leoTOWX2c/IbevjQM1AGJUrgHU3bOMSnfHn/6Q5IhZT8w0E64dd/BEMsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbe26e3bad3475ddeebccaed5d60b7be26b85386cb5a87755810edd577bc279e","last_reissued_at":"2026-05-18T02:21:50.329457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:50.329457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conformal invariance of loops in the double-dimer model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Richard Kenyon","submitted_at":"2011-05-20T19:19:42Z","abstract_excerpt":"The dimer model is the study of random dimer covers (perfect matchings) of a graph. 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