{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:XOTH7EI6DZC2TUVLOE3JFLGW6Z","short_pith_number":"pith:XOTH7EI6","canonical_record":{"source":{"id":"2607.29495","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-31T15:03:00Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"bd2cec7a43ec831b7cfb2374bff58906998d58f77c37f9a1a317c4c246f022f0","abstract_canon_sha256":"48ea9092f5c93fe40bfaccf92c5694a4c0a2a0a57cdbeb7b91a5a2c16c6f0fa0"},"schema_version":"1.0"},"canonical_sha256":"bba67f911e1e45a9d2ab713692acd6f65077d6b8de1c38d1f28a8d484abc5b33","source":{"kind":"arxiv","id":"2607.29495","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29495","created_at":"2026-08-03T01:36:10Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29495v1","created_at":"2026-08-03T01:36:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29495","created_at":"2026-08-03T01:36:10Z"},{"alias_kind":"pith_short_12","alias_value":"XOTH7EI6DZC2","created_at":"2026-08-03T01:36:10Z"},{"alias_kind":"pith_short_16","alias_value":"XOTH7EI6DZC2TUVL","created_at":"2026-08-03T01:36:10Z"},{"alias_kind":"pith_short_8","alias_value":"XOTH7EI6","created_at":"2026-08-03T01:36:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:XOTH7EI6DZC2TUVLOE3JFLGW6Z","target":"record","payload":{"canonical_record":{"source":{"id":"2607.29495","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-31T15:03:00Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"bd2cec7a43ec831b7cfb2374bff58906998d58f77c37f9a1a317c4c246f022f0","abstract_canon_sha256":"48ea9092f5c93fe40bfaccf92c5694a4c0a2a0a57cdbeb7b91a5a2c16c6f0fa0"},"schema_version":"1.0"},"canonical_sha256":"bba67f911e1e45a9d2ab713692acd6f65077d6b8de1c38d1f28a8d484abc5b33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:36:10.018929Z","signature_b64":"8wtG9U1YgxPZMpETYHyjw+jOGDuq7B2YmTjKyOSTyLo3Qve3M0AhIH0jqsGOQXcNJjp2QDMKCBPbIiEXuxrOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bba67f911e1e45a9d2ab713692acd6f65077d6b8de1c38d1f28a8d484abc5b33","last_reissued_at":"2026-08-03T01:36:10.017410Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:36:10.017410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.29495","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-03T01:36:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v5l8mA5icGlfildtJ8EBennoSrzIOip76SoVTAHoLdacsmOuJqxr6MWfn7MavX86hgRvDc532zmywTP58oPMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T18:36:54.802682Z"},"content_sha256":"2e36364aa40b7c2b5e24619e786fe6abe72878110409a9f79ab4bb738dc4a5a3","schema_version":"1.0","event_id":"sha256:2e36364aa40b7c2b5e24619e786fe6abe72878110409a9f79ab4bb738dc4a5a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:XOTH7EI6DZC2TUVLOE3JFLGW6Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast Mixing for Low-Temperature Potts Models via Poisson Trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.PR","authors_text":"Andreas Galanis, Leslie Ann Goldberg, Paulina Smolarova, Xandru Mifsud, Xusheng Zhang, Zongchen Chen","submitted_at":"2026-07-31T15:03:00Z","abstract_excerpt":"The $q$-state ferromagnetic Potts model on a graph $G$ is a probability distribution on all $q$-colourings of $G$ that favours many monochromatic edges. Approximate sampling from the Potts model is a central problem in the study of spin systems on sparse graphs, especially in the low-temperature regime, where the model strongly favours ordered configurations, often creating bottlenecks that make Markov-chain sampling inefficient or difficult to analyse.\n  We focus on the sparse random graph $G(n,d/n)$. The local neighbourhoods of $G(n,d/n)$ are tree-like, but the relevant underlying graph is a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29495","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.29495/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-03T01:36:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/QTaDpag+EM3AkbJBIL6rJyAQJrRnqxcevo6Ri2UDnINKauXgUa/WTaxzlHpbOCFTHQchezg92q9c9PM3uYfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T18:36:54.803214Z"},"content_sha256":"bf2f80a7a1ff12492aa3a63c26de2c340c8b25dddae84d2ccd328b0e4c044a14","schema_version":"1.0","event_id":"sha256:bf2f80a7a1ff12492aa3a63c26de2c340c8b25dddae84d2ccd328b0e4c044a14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XOTH7EI6DZC2TUVLOE3JFLGW6Z/bundle.json","state_url":"https://pith.science/pith/XOTH7EI6DZC2TUVLOE3JFLGW6Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XOTH7EI6DZC2TUVLOE3JFLGW6Z/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T18:36:54Z","links":{"resolver":"https://pith.science/pith/XOTH7EI6DZC2TUVLOE3JFLGW6Z","bundle":"https://pith.science/pith/XOTH7EI6DZC2TUVLOE3JFLGW6Z/bundle.json","state":"https://pith.science/pith/XOTH7EI6DZC2TUVLOE3JFLGW6Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XOTH7EI6DZC2TUVLOE3JFLGW6Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XOTH7EI6DZC2TUVLOE3JFLGW6Z","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":"48ea9092f5c93fe40bfaccf92c5694a4c0a2a0a57cdbeb7b91a5a2c16c6f0fa0","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-31T15:03:00Z","title_canon_sha256":"bd2cec7a43ec831b7cfb2374bff58906998d58f77c37f9a1a317c4c246f022f0"},"schema_version":"1.0","source":{"id":"2607.29495","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29495","created_at":"2026-08-03T01:36:10Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29495v1","created_at":"2026-08-03T01:36:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29495","created_at":"2026-08-03T01:36:10Z"},{"alias_kind":"pith_short_12","alias_value":"XOTH7EI6DZC2","created_at":"2026-08-03T01:36:10Z"},{"alias_kind":"pith_short_16","alias_value":"XOTH7EI6DZC2TUVL","created_at":"2026-08-03T01:36:10Z"},{"alias_kind":"pith_short_8","alias_value":"XOTH7EI6","created_at":"2026-08-03T01:36:10Z"}],"graph_snapshots":[{"event_id":"sha256:bf2f80a7a1ff12492aa3a63c26de2c340c8b25dddae84d2ccd328b0e4c044a14","target":"graph","created_at":"2026-08-03T01:36:10Z","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/2607.29495/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $q$-state ferromagnetic Potts model on a graph $G$ is a probability distribution on all $q$-colourings of $G$ that favours many monochromatic edges. Approximate sampling from the Potts model is a central problem in the study of spin systems on sparse graphs, especially in the low-temperature regime, where the model strongly favours ordered configurations, often creating bottlenecks that make Markov-chain sampling inefficient or difficult to analyse.\n  We focus on the sparse random graph $G(n,d/n)$. The local neighbourhoods of $G(n,d/n)$ are tree-like, but the relevant underlying graph is a","authors_text":"Andreas Galanis, Leslie Ann Goldberg, Paulina Smolarova, Xandru Mifsud, Xusheng Zhang, Zongchen Chen","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-31T15:03:00Z","title":"Fast Mixing for Low-Temperature Potts Models via Poisson Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29495","kind":"arxiv","version":1},"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":"sha256:2e36364aa40b7c2b5e24619e786fe6abe72878110409a9f79ab4bb738dc4a5a3","target":"record","created_at":"2026-08-03T01:36:10Z","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":"48ea9092f5c93fe40bfaccf92c5694a4c0a2a0a57cdbeb7b91a5a2c16c6f0fa0","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-31T15:03:00Z","title_canon_sha256":"bd2cec7a43ec831b7cfb2374bff58906998d58f77c37f9a1a317c4c246f022f0"},"schema_version":"1.0","source":{"id":"2607.29495","kind":"arxiv","version":1}},"canonical_sha256":"bba67f911e1e45a9d2ab713692acd6f65077d6b8de1c38d1f28a8d484abc5b33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bba67f911e1e45a9d2ab713692acd6f65077d6b8de1c38d1f28a8d484abc5b33","first_computed_at":"2026-08-03T01:36:10.017410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:36:10.017410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8wtG9U1YgxPZMpETYHyjw+jOGDuq7B2YmTjKyOSTyLo3Qve3M0AhIH0jqsGOQXcNJjp2QDMKCBPbIiEXuxrOBQ==","signature_status":"signed_v1","signed_at":"2026-08-03T01:36:10.018929Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.29495","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e36364aa40b7c2b5e24619e786fe6abe72878110409a9f79ab4bb738dc4a5a3","sha256:bf2f80a7a1ff12492aa3a63c26de2c340c8b25dddae84d2ccd328b0e4c044a14"],"state_sha256":"70e360cb3ff6d4b1f59229ddf8d298dfe00fc29cbbebddfce108eb654126f703"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLo6TD+lfTWyfg7Iztzq5eXZU9hqQO55QWrgnMyVWorBbTH+tHA9kr+BVUQLaq6wsxPhCVx0bDNMltqloGR+AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T18:36:54.809068Z","bundle_sha256":"5e69cd6f325f268f8c73347a6a479a79dc2f35a7a4d713aac57baf19132e53b5"}}