{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FBUOXLSWYBW3VK55SJLP4BQCWQ","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":"4978b1640a796107fa236d6a60fb5acdd7b4ba09ec674cad3dcf571da37564f7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-30T17:16:36Z","title_canon_sha256":"0de0b6633d5e3d13c09ff81ab8076c17a876fd79e0dfe3c2c27966a175ab51e4"},"schema_version":"1.0","source":{"id":"1312.7785","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7785","created_at":"2026-05-18T03:03:33Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7785v1","created_at":"2026-05-18T03:03:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7785","created_at":"2026-05-18T03:03:33Z"},{"alias_kind":"pith_short_12","alias_value":"FBUOXLSWYBW3","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FBUOXLSWYBW3VK55","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FBUOXLSW","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:960cf3ca23b88969c3a18aa14310243c5f7ff68f7d2188a85cf4c3e2c63ac21b","target":"graph","created_at":"2026-05-18T03:03:33Z","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":"We consider the FK-Ising model in two dimensions at criticality. We obtain bounds on crossing probabilities of arbitrary topological rectangles, uniform with respect to the boundary conditions, generalizing results of [DCHN11] and [CS12]. Our result relies on new discrete complex analysis techniques, introduced in [Che12]. We detail some applications, in particular the computation of so-called universal exponents, the proof of quasi-multiplicativity properties of arm probabilities, and bounds on crossing probabilities for the classical Ising model.","authors_text":"Cl\\'ement Hongler, Dmitry Chelkak, Hugo Duminil-Copin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-30T17:16:36Z","title":"Crossing probabilities in topological rectangles for the critical planar FK-Ising model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7785","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":"sha256:25ce81b0120681b0059dd614c07fc426b4d212165a0545e7138d97ce607d2042","target":"record","created_at":"2026-05-18T03:03:33Z","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":"4978b1640a796107fa236d6a60fb5acdd7b4ba09ec674cad3dcf571da37564f7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-30T17:16:36Z","title_canon_sha256":"0de0b6633d5e3d13c09ff81ab8076c17a876fd79e0dfe3c2c27966a175ab51e4"},"schema_version":"1.0","source":{"id":"1312.7785","kind":"arxiv","version":1}},"canonical_sha256":"2868ebae56c06dbaabbd9256fe0602b4192bd6c00b9fa5b711973df1e1fcdb4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2868ebae56c06dbaabbd9256fe0602b4192bd6c00b9fa5b711973df1e1fcdb4e","first_computed_at":"2026-05-18T03:03:33.710893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:33.710893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ovcth+teLinxulWhFItQLRagxnfpKUvmavvnc4pcMoa9uy/HfA0WVaL2ACZZzSbsiqu/TYjYr1CSPeiMrgF8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:33.711361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7785","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25ce81b0120681b0059dd614c07fc426b4d212165a0545e7138d97ce607d2042","sha256:960cf3ca23b88969c3a18aa14310243c5f7ff68f7d2188a85cf4c3e2c63ac21b"],"state_sha256":"c7c17847d9a82370a6ef8fe7d5af309b68272335e2d3d2a2cf47bdadd9915036"}