{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HJITBXWIYDV2JZHW5UB6VZACOO","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":"5e52d1c056592ea1c0f5ed6498cd72b8c0d5d0e0e6692bd7482299a528fb4847","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-05-03T16:55:54Z","title_canon_sha256":"df7ff10196a96c866e3d0884a1fd83282b9780438cf8e50cff778e47125f415d"},"schema_version":"1.0","source":{"id":"1305.0776","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0776","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0776v2","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0776","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"HJITBXWIYDV2","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HJITBXWIYDV2JZHW","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HJITBXWI","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:85b260761b1c3f0c1972a02ae8b7e9d0efeb3721ae931db5add64dac3ac50670","target":"graph","created_at":"2026-05-18T02:50:24Z","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 present several results on the mixing time of the Glauber dynamics for sampling from the Gibbs distribution in the ferromagnetic Potts model. At a fixed temperature and interaction strength, we study the interplay between the maximum degree ($\\Delta$) of the underlying graph and the number of colours or spins ($q$) in determining whether the dynamics mixes rapidly or not. We find a lower bound $L$ on the number of colours such that Glauber dynamics is rapidly mixing if at least $L$ colours are used. We give a closely-matching upper bound $U$ on the number of colours such that with probabili","authors_text":"Catherine Greenhill, Magnus Bordewich, Viresh Patel","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-05-03T16:55:54Z","title":"Mixing of the Glauber dynamics for the ferromagnetic Potts model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0776","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":"sha256:1fb21259d5a1559560774c7eccc44d69616250ca0761895287704e465e935b58","target":"record","created_at":"2026-05-18T02:50:24Z","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":"5e52d1c056592ea1c0f5ed6498cd72b8c0d5d0e0e6692bd7482299a528fb4847","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-05-03T16:55:54Z","title_canon_sha256":"df7ff10196a96c866e3d0884a1fd83282b9780438cf8e50cff778e47125f415d"},"schema_version":"1.0","source":{"id":"1305.0776","kind":"arxiv","version":2}},"canonical_sha256":"3a5130dec8c0eba4e4f6ed03eae4027399310103c33d92c35a635e09a4336bab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a5130dec8c0eba4e4f6ed03eae4027399310103c33d92c35a635e09a4336bab","first_computed_at":"2026-05-18T02:50:24.395454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:24.395454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hch1MVHQMB0GwA4RHb4EebFc217oQQLzZ1qTjAOWoR4LG97xqDmgZ1cgkBPhUPCdObA8CiaYrKME9yYG73HeBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:24.395858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0776","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fb21259d5a1559560774c7eccc44d69616250ca0761895287704e465e935b58","sha256:85b260761b1c3f0c1972a02ae8b7e9d0efeb3721ae931db5add64dac3ac50670"],"state_sha256":"8a9570194a2729c0eaea8ea8f53c1c586ebaaa563c7bf9e6a2421a80ef499c28"}