{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:IPCMIEPSX2EOIKMZXPQGACP3HG","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":"38556683b18202b12cfff9a1649b8094106a9b5a8ad3316bad3cbb782c5f1547","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2003-08-28T20:13:52Z","title_canon_sha256":"0c72dc284e943c67e00efe05f8b2b85fa1b1686875b96d8267c3ba8d549bf6f5"},"schema_version":"1.0","source":{"id":"math/0308284","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0308284","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0308284v3","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0308284","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"IPCMIEPSX2EO","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"IPCMIEPSX2EOIKMZ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"IPCMIEPS","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:066524605278bf43e9ccce5980f744b02fe1e57a1e277576cff2cfec0abb02ef","target":"graph","created_at":"2026-05-18T01:05:28Z","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 study continuous time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with $n$ vertices and of bounded degree. We show that the relaxation time\n (defined as the reciprocal of the spectral gap $|\\lambda_1-\\lambda_2|$) for the dynamics on trees and on planar hyperbolic graphs, is polynomial in $n$. For these hyperbolic graphs, this yields a general polynomial sampling algorithm for random configurations. We then show that if the relaxation time $\\tau_2$ satisfies $\\tau_2=O(1)$, then the correlation coefficient, ","authors_text":"Claire Kenyon, Elchanan Mossel, Noam Berger, Yuval Peres","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2003-08-28T20:13:52Z","title":"Glauber Dynamics on Trees and Hyperbolic Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0308284","kind":"arxiv","version":3},"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:e1dc34476993abc681c36f58841a5414cba8ff191fc01b6a0aa7952e9ed41c06","target":"record","created_at":"2026-05-18T01:05:28Z","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":"38556683b18202b12cfff9a1649b8094106a9b5a8ad3316bad3cbb782c5f1547","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2003-08-28T20:13:52Z","title_canon_sha256":"0c72dc284e943c67e00efe05f8b2b85fa1b1686875b96d8267c3ba8d549bf6f5"},"schema_version":"1.0","source":{"id":"math/0308284","kind":"arxiv","version":3}},"canonical_sha256":"43c4c411f2be88e42999bbe06009fb39a1a3c1238b1b1879572ad032c6064568","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43c4c411f2be88e42999bbe06009fb39a1a3c1238b1b1879572ad032c6064568","first_computed_at":"2026-05-18T01:05:28.680408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:28.680408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0O2NGABBZ4JWvcB/VRaZS90L0X5Vtbwx3/luaRh2fmVLPzm20w2RGl++AYbfOndJt/LNkjowpD/BUDn+FjxQDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:28.681428Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0308284","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1dc34476993abc681c36f58841a5414cba8ff191fc01b6a0aa7952e9ed41c06","sha256:066524605278bf43e9ccce5980f744b02fe1e57a1e277576cff2cfec0abb02ef"],"state_sha256":"daa1f0d3d1769cfef5d72532d4b684cec8584883ef385338a60ebcc165b50575"}