{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QHEYRJLUXAVW2DFCGZDGRLFTM5","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":"b571466efa425d981d35cd924828891f3224b6d9754da668d0b6509d2b768c23","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-09-20T02:42:47Z","title_canon_sha256":"99f19808adc921aa57f2c0879ad704c0775f762aa30f3593e30a876046dc2c8b"},"schema_version":"1.0","source":{"id":"1909.09298","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.09298","created_at":"2026-07-05T04:46:29Z"},{"alias_kind":"arxiv_version","alias_value":"1909.09298v3","created_at":"2026-07-05T04:46:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.09298","created_at":"2026-07-05T04:46:29Z"},{"alias_kind":"pith_short_12","alias_value":"QHEYRJLUXAVW","created_at":"2026-07-05T04:46:29Z"},{"alias_kind":"pith_short_16","alias_value":"QHEYRJLUXAVW2DFC","created_at":"2026-07-05T04:46:29Z"},{"alias_kind":"pith_short_8","alias_value":"QHEYRJLU","created_at":"2026-07-05T04:46:29Z"}],"graph_snapshots":[{"event_id":"sha256:1ba6f8b64dce04a22a4d334db6d9531ca9fe44081a773cb174df2ea0474ec150","target":"graph","created_at":"2026-07-05T04:46:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.09298/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For $d \\ge 2$ and all $q\\geq q_{0}(d)$ we give an efficient algorithm to approximately sample from the $q$-state ferromagnetic Potts and random cluster models on finite tori $(\\mathbb Z / n \\mathbb Z )^d$ for any inverse temperature $\\beta\\geq 0$. This shows that the physical phase transition of the Potts model presents no algorithmic barrier to efficient sampling, and stands in contrast to Markov chain mixing time results: the Glauber dynamics mix slowly at and below the critical temperature, and the Swendsen--Wang dynamics mix slowly at the critical temperature. We also provide an efficient ","authors_text":"Christian Borgs, Jennifer Chayes, Prasad Tetali, Tyler Helmuth, Will Perkins","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-09-20T02:42:47Z","title":"Efficient sampling and counting algorithms for the Potts model on $\\mathbb Z^d$ at all temperatures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.09298","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":"sha256:35cecd815b7c1d29423f29c426a46152a3ab330100b8eb1c627ce8376b396359","target":"record","created_at":"2026-07-05T04:46:29Z","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":"b571466efa425d981d35cd924828891f3224b6d9754da668d0b6509d2b768c23","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-09-20T02:42:47Z","title_canon_sha256":"99f19808adc921aa57f2c0879ad704c0775f762aa30f3593e30a876046dc2c8b"},"schema_version":"1.0","source":{"id":"1909.09298","kind":"arxiv","version":3}},"canonical_sha256":"81c988a574b82b6d0ca2364668acb3677b74b9f7fba03356f124e266928360da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81c988a574b82b6d0ca2364668acb3677b74b9f7fba03356f124e266928360da","first_computed_at":"2026-07-05T04:46:29.156755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:46:29.156755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QcCr0WT1GMbMNmQTmdJ6yl7VGOUaPI8gJzu/ujs0N4DSGAcswSN2LovJkDloZGX+3U+HXo8b0F5MewbosxLNDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:46:29.157151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.09298","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35cecd815b7c1d29423f29c426a46152a3ab330100b8eb1c627ce8376b396359","sha256:1ba6f8b64dce04a22a4d334db6d9531ca9fe44081a773cb174df2ea0474ec150"],"state_sha256":"fa52c7f9eadf5d40dba20e3c723bb6d28038fefad03bdd7b3ad18ac0b5dc0383"}