{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:5WZLRWALX7LJSEAK2TYUN5VFD7","short_pith_number":"pith:5WZLRWAL","schema_version":"1.0","canonical_sha256":"edb2b8d80bbfd699100ad4f146f6a51fe34c3002d05885ca23f2699b788ff7df","source":{"kind":"arxiv","id":"1211.4825","version":2},"attestation_state":"computed","paper":{"title":"Height representation of XOR-Ising loops via bipartite dimers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"B\\'eatrice de Tili\\`ere, C\\'edric Boutillier","submitted_at":"2012-11-20T18:17:29Z","abstract_excerpt":"The XOR-Ising model on a graph consists of random spin configurations on vertices of the graph obtained by taking the product at each vertex of the spins of two independent Ising models. In this paper, we explicitly relate loop configurations of the XOR-Ising model and those of a dimer model living on a decorated, bipartite version of the Ising graph. This result is proved for graphs embedded in compact surfaces of genus g.\n  Using this fact, we then prove that XOR-Ising loops have the same law as level lines of the height function of this bipartite dimer model. At criticality, the height func"},"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":"1211.4825","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-20T18:17:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3e82dbd08ff979be3b0f532e3293520a8af397738429be0a1002772b2acc676b","abstract_canon_sha256":"83b85c0946508c71b9978ca340c62b14f62a4306726e0c1b165e4f1366438672"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:37.108627Z","signature_b64":"HKldSU1WnJHGpu0pGsuhe8nJf0i2QaULbxfdNzkTWbzPwZXQO+SrCkxFRBjqUcZEaWNg5GWY+3TR0A04JlCKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edb2b8d80bbfd699100ad4f146f6a51fe34c3002d05885ca23f2699b788ff7df","last_reissued_at":"2026-05-18T02:43:37.107929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:37.107929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Height representation of XOR-Ising loops via bipartite dimers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"B\\'eatrice de Tili\\`ere, C\\'edric Boutillier","submitted_at":"2012-11-20T18:17:29Z","abstract_excerpt":"The XOR-Ising model on a graph consists of random spin configurations on vertices of the graph obtained by taking the product at each vertex of the spins of two independent Ising models. In this paper, we explicitly relate loop configurations of the XOR-Ising model and those of a dimer model living on a decorated, bipartite version of the Ising graph. This result is proved for graphs embedded in compact surfaces of genus g.\n  Using this fact, we then prove that XOR-Ising loops have the same law as level lines of the height function of this bipartite dimer model. At criticality, the height func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4825","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.4825","created_at":"2026-05-18T02:43:37.108031+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.4825v2","created_at":"2026-05-18T02:43:37.108031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4825","created_at":"2026-05-18T02:43:37.108031+00:00"},{"alias_kind":"pith_short_12","alias_value":"5WZLRWALX7LJ","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"5WZLRWALX7LJSEAK","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"5WZLRWAL","created_at":"2026-05-18T12:26:56.085431+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5WZLRWALX7LJSEAK2TYUN5VFD7","json":"https://pith.science/pith/5WZLRWALX7LJSEAK2TYUN5VFD7.json","graph_json":"https://pith.science/api/pith-number/5WZLRWALX7LJSEAK2TYUN5VFD7/graph.json","events_json":"https://pith.science/api/pith-number/5WZLRWALX7LJSEAK2TYUN5VFD7/events.json","paper":"https://pith.science/paper/5WZLRWAL"},"agent_actions":{"view_html":"https://pith.science/pith/5WZLRWALX7LJSEAK2TYUN5VFD7","download_json":"https://pith.science/pith/5WZLRWALX7LJSEAK2TYUN5VFD7.json","view_paper":"https://pith.science/paper/5WZLRWAL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.4825&json=true","fetch_graph":"https://pith.science/api/pith-number/5WZLRWALX7LJSEAK2TYUN5VFD7/graph.json","fetch_events":"https://pith.science/api/pith-number/5WZLRWALX7LJSEAK2TYUN5VFD7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5WZLRWALX7LJSEAK2TYUN5VFD7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5WZLRWALX7LJSEAK2TYUN5VFD7/action/storage_attestation","attest_author":"https://pith.science/pith/5WZLRWALX7LJSEAK2TYUN5VFD7/action/author_attestation","sign_citation":"https://pith.science/pith/5WZLRWALX7LJSEAK2TYUN5VFD7/action/citation_signature","submit_replication":"https://pith.science/pith/5WZLRWALX7LJSEAK2TYUN5VFD7/action/replication_record"}},"created_at":"2026-05-18T02:43:37.108031+00:00","updated_at":"2026-05-18T02:43:37.108031+00:00"}