{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LXUONZRYX4PW4D4OPFONFJWMHP","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":"09293551fec6c8fe4e9052034d697b5c3e460600c0380b3ff7188760f80f53d5","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-21T00:15:24Z","title_canon_sha256":"f5887c22115c0070ccfc77696e00992afc5c4334f73339776574d79f1fa96648"},"schema_version":"1.0","source":{"id":"1205.4472","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4472","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4472v3","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4472","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"LXUONZRYX4PW","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LXUONZRYX4PW4D4O","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LXUONZRY","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:2318092665cd47d3fda6860f81e4bf4c5e7cbe389ae4bd34e03fd614ee1ea5f8","target":"graph","created_at":"2026-05-18T02:42:39Z","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 prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More precisely, we show the existence of (at least) three infinite-volume Gibbs measures, which exhibit spontaneous magnetization in the sense that vertices in one sublattice have a higher probability to be in one state than in either of the other two states. For the special case of the diced lattice, we give a good rigorous lower bound on this probability, based on ","authors_text":"Alan D. Sokal, Jan M. Swart, Roman Koteck\\'y","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-21T00:15:24Z","title":"Entropy-driven phase transition in low-temperature antiferromagnetic Potts models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4472","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":"sha256:631c274fc91c8328d481394e32c8ea48af8499f91ccd2e442df8af130032f221","target":"record","created_at":"2026-05-18T02:42:39Z","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":"09293551fec6c8fe4e9052034d697b5c3e460600c0380b3ff7188760f80f53d5","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-21T00:15:24Z","title_canon_sha256":"f5887c22115c0070ccfc77696e00992afc5c4334f73339776574d79f1fa96648"},"schema_version":"1.0","source":{"id":"1205.4472","kind":"arxiv","version":3}},"canonical_sha256":"5de8e6e638bf1f6e0f8e795cd2a6cc3bc5603c4ca9f47931e974d64466b6612e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5de8e6e638bf1f6e0f8e795cd2a6cc3bc5603c4ca9f47931e974d64466b6612e","first_computed_at":"2026-05-18T02:42:39.814219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:39.814219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W0GMQgPUczUQxy85c/Wklu9I/4qG8YT6XGsvLlkkOwPhv+krbfC2Eu1FopCGWO+EBSeVyA6Wv2oCX1dkhHLzBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:39.814727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4472","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:631c274fc91c8328d481394e32c8ea48af8499f91ccd2e442df8af130032f221","sha256:2318092665cd47d3fda6860f81e4bf4c5e7cbe389ae4bd34e03fd614ee1ea5f8"],"state_sha256":"3c628b9a4fc19cae912b96e6c18c70181a68b9d5bac0dad0ca25d64410ca8c13"}