{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:3GPFNSFJT3WB56OSSUTI2GDSWN","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":"e9170281631e426f29812d405a508cceab4d666d586f89604114bb0be668c198","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2009-03-03T03:55:20Z","title_canon_sha256":"37fbcb80009dedfd86ada6ddf363fa9727cd1fc1f54f24559e2432f62e4c7397"},"schema_version":"1.0","source":{"id":"0903.0438","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.0438","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"0903.0438v4","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.0438","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"3GPFNSFJT3WB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"3GPFNSFJT3WB56OS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"3GPFNSFJ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:a50f85081b0393a9ead09b7869fa394ca2b675b61069f4e41f3825604127f0d0","target":"graph","created_at":"2026-05-18T04:39:59Z","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 analytically show the percolation thresholds of the Fortuin-Kasteleyn cluster for the Edwards-Anderson Ising model on random graphs with arbitrary degree distributions. The results on the Nishimori line are shown. We obtain the results for the +-J model, the diluted +-J model, and the Gaussian model, by applying an extension of a criterion for the random graphs with arbitrary degree distributions. The results for the infinite-range $\\pm J$ model and the Sherrington-Kirkpatrick model are also shown.","authors_text":"Chiaki Yamaguchi","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2009-03-03T03:55:20Z","title":"Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the Edwards-Anderson Ising Model on Complex Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0438","kind":"arxiv","version":4},"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":"sha256:25ec7fe9de9fd981c8ee6e519c912f5a1f15e80b37613b10529254b897d4ba6c","target":"record","created_at":"2026-05-18T04:39:59Z","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":"e9170281631e426f29812d405a508cceab4d666d586f89604114bb0be668c198","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2009-03-03T03:55:20Z","title_canon_sha256":"37fbcb80009dedfd86ada6ddf363fa9727cd1fc1f54f24559e2432f62e4c7397"},"schema_version":"1.0","source":{"id":"0903.0438","kind":"arxiv","version":4}},"canonical_sha256":"d99e56c8a99eec1ef9d295268d1872b347f691365127679f2b2b022e0c28792b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d99e56c8a99eec1ef9d295268d1872b347f691365127679f2b2b022e0c28792b","first_computed_at":"2026-05-18T04:39:59.618423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:59.618423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fQEneec7ZY4to9uPvaoguuLc46lObaDAvbA3QU7a4M9EjeHoaRr8BEZZBe0m/hdizmSuC8nnAxQhbJDYO0oRBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:59.618869Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.0438","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25ec7fe9de9fd981c8ee6e519c912f5a1f15e80b37613b10529254b897d4ba6c","sha256:a50f85081b0393a9ead09b7869fa394ca2b675b61069f4e41f3825604127f0d0"],"state_sha256":"417229eb7aada27b559d550026f0d523d521bc16799526f032b56ce55bf7af1f"}