{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:25SHVMX4XJY4UVM4O7SM6BS3RG","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":"df57a459ae57b574374df05281aed010f5e1825623d3048f73bbfe14d10f90eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-18T23:34:03Z","title_canon_sha256":"c64926359816481ce2449bfc6dcd6e5e99fb6421793e9cb51a4ea13404efcd47"},"schema_version":"1.0","source":{"id":"1412.6180","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6180","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6180v2","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6180","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"pith_short_12","alias_value":"25SHVMX4XJY4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"25SHVMX4XJY4UVM4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"25SHVMX4","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:2789ecb7b86eae290f194929f1d5b70e9115ac336708b3633b3405690f0d22b1","target":"graph","created_at":"2026-05-18T01:37:01Z","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":"The random-cluster model is a unifying framework for studying random graphs, spin systems in physics and random spanning trees. The model is closely related to, though much more general than the classical Ising and Potts models, but its dynamics are much less well understood. In this paper we study a natural non-local Markov chain known as the Chayes-Machta dynamics for the mean-field case of the random-cluster model, and identify a critical regime $(\\lambda_s,\\lambda_S)$ of the model parameter $\\lambda$ in which the dynamics undergoes an exponential slowdown. Namely, we prove that the mixing ","authors_text":"Alistair Sinclair, Antonio Blanca","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-18T23:34:03Z","title":"Dynamics for the mean-field random-cluster model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6180","kind":"arxiv","version":2},"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:dcc86d40f67399a1d431b948f9e652f4f30e0cd49d88ecd51da98d2f30e74b35","target":"record","created_at":"2026-05-18T01:37:01Z","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":"df57a459ae57b574374df05281aed010f5e1825623d3048f73bbfe14d10f90eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-18T23:34:03Z","title_canon_sha256":"c64926359816481ce2449bfc6dcd6e5e99fb6421793e9cb51a4ea13404efcd47"},"schema_version":"1.0","source":{"id":"1412.6180","kind":"arxiv","version":2}},"canonical_sha256":"d7647ab2fcba71ca559c77e4cf065b89a2afde8e56cd31b9ad3c7a94891e7b4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7647ab2fcba71ca559c77e4cf065b89a2afde8e56cd31b9ad3c7a94891e7b4f","first_computed_at":"2026-05-18T01:37:01.922153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:01.922153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tWVQ+vDgpIHuhk+/JN+rXyk81HfLevyjfOXyZxRVvzhEXq5Js4aM8lH91sxKWB46dkZZqVntUAeSifV1FYrmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:01.922712Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6180","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcc86d40f67399a1d431b948f9e652f4f30e0cd49d88ecd51da98d2f30e74b35","sha256:2789ecb7b86eae290f194929f1d5b70e9115ac336708b3633b3405690f0d22b1"],"state_sha256":"e10c16e0495f2e8089f8f01d29ca95baf92710cc7d309cafe4088021776698c0"}