{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:NC54KMIUELJ6MPSBGGIQAWJGXQ","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":"2c18067ee068987791c067ad5bbfac6c0f0222ff0f6aad62231e486653ca34f6","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.PR","submitted_at":"1999-12-16T23:17:11Z","title_canon_sha256":"f1577a2cf6c89701aceaa4f044829e6f1db03f588e9eb020cfff5ef072c9a3e2"},"schema_version":"1.0","source":{"id":"math/9912136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9912136","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/9912136v1","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9912136","created_at":"2026-05-18T04:08:35Z"},{"alias_kind":"pith_short_12","alias_value":"NC54KMIUELJ6","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"NC54KMIUELJ6MPSB","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"NC54KMIU","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:9715898aedd7f88c36e8a264943442ab436cb581e41dbc61adc36c5f46071774","target":"graph","created_at":"2026-05-18T04:08:35Z","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 contour representation of the infinite volume Ising model at low temperature. Fix a subset V of Z^d, and a (large) N such that calling G_{N,V} the set of contours of length at least N intersecting V, there are in average one contour in G_{N,V} under the infinite volume \"plus\" measure. We find bounds on the total variation distance between the law of the contours of lenght at least N intersecting V under the \"plus\" measure and a Poisson process. The proof builds on the Chen-Stein method as presented by Arratia, Goldstein and Gordon. The control of the correlations is obtained th","authors_text":"Pablo A. Ferrari, Pierre Picco","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"1999-12-16T23:17:11Z","title":"Poisson approximation for large-contours in low-temperature Ising models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9912136","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":"sha256:5ecf5a41c2b1e114e9442e0bd6cea8cbbce776d9f76b1e54f8a18cb7e9813b2d","target":"record","created_at":"2026-05-18T04:08:35Z","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":"2c18067ee068987791c067ad5bbfac6c0f0222ff0f6aad62231e486653ca34f6","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.PR","submitted_at":"1999-12-16T23:17:11Z","title_canon_sha256":"f1577a2cf6c89701aceaa4f044829e6f1db03f588e9eb020cfff5ef072c9a3e2"},"schema_version":"1.0","source":{"id":"math/9912136","kind":"arxiv","version":1}},"canonical_sha256":"68bbc5311422d3e63e413191005926bc39d5078bf5720060834b63a5579361d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68bbc5311422d3e63e413191005926bc39d5078bf5720060834b63a5579361d7","first_computed_at":"2026-05-18T04:08:35.451441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:35.451441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XDVfqPwEP6T8iJrn5bmk9hhbLDfUU1jEbNo2qrHEi72tDdNdvVIAqftbRHDDKnnhGY7IwopgGlIOEvBGbVAAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:35.452090Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9912136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ecf5a41c2b1e114e9442e0bd6cea8cbbce776d9f76b1e54f8a18cb7e9813b2d","sha256:9715898aedd7f88c36e8a264943442ab436cb581e41dbc61adc36c5f46071774"],"state_sha256":"754ee51374fdd8794772d6f071011e7811a845915376549769c947454c57c68d"}