{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LXUONZRYX4PW4D4OPFONFJWMHP","short_pith_number":"pith:LXUONZRY","schema_version":"1.0","canonical_sha256":"5de8e6e638bf1f6e0f8e795cd2a6cc3bc5603c4ca9f47931e974d64466b6612e","source":{"kind":"arxiv","id":"1205.4472","version":3},"attestation_state":"computed","paper":{"title":"Entropy-driven phase transition in low-temperature antiferromagnetic Potts models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Alan D. Sokal, Jan M. Swart, Roman Koteck\\'y","submitted_at":"2012-05-21T00:15:24Z","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.4472","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-21T00:15:24Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"f5887c22115c0070ccfc77696e00992afc5c4334f73339776574d79f1fa96648","abstract_canon_sha256":"09293551fec6c8fe4e9052034d697b5c3e460600c0380b3ff7188760f80f53d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:39.814727Z","signature_b64":"W0GMQgPUczUQxy85c/Wklu9I/4qG8YT6XGsvLlkkOwPhv+krbfC2Eu1FopCGWO+EBSeVyA6Wv2oCX1dkhHLzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5de8e6e638bf1f6e0f8e795cd2a6cc3bc5603c4ca9f47931e974d64466b6612e","last_reissued_at":"2026-05-18T02:42:39.814219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:39.814219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy-driven phase transition in low-temperature antiferromagnetic Potts models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Alan D. Sokal, Jan M. Swart, Roman Koteck\\'y","submitted_at":"2012-05-21T00:15:24Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4472","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1205.4472","created_at":"2026-05-18T02:42:39.814278+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.4472v3","created_at":"2026-05-18T02:42:39.814278+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4472","created_at":"2026-05-18T02:42:39.814278+00:00"},{"alias_kind":"pith_short_12","alias_value":"LXUONZRYX4PW","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LXUONZRYX4PW4D4O","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LXUONZRY","created_at":"2026-05-18T12:27:14.488303+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LXUONZRYX4PW4D4OPFONFJWMHP","json":"https://pith.science/pith/LXUONZRYX4PW4D4OPFONFJWMHP.json","graph_json":"https://pith.science/api/pith-number/LXUONZRYX4PW4D4OPFONFJWMHP/graph.json","events_json":"https://pith.science/api/pith-number/LXUONZRYX4PW4D4OPFONFJWMHP/events.json","paper":"https://pith.science/paper/LXUONZRY"},"agent_actions":{"view_html":"https://pith.science/pith/LXUONZRYX4PW4D4OPFONFJWMHP","download_json":"https://pith.science/pith/LXUONZRYX4PW4D4OPFONFJWMHP.json","view_paper":"https://pith.science/paper/LXUONZRY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.4472&json=true","fetch_graph":"https://pith.science/api/pith-number/LXUONZRYX4PW4D4OPFONFJWMHP/graph.json","fetch_events":"https://pith.science/api/pith-number/LXUONZRYX4PW4D4OPFONFJWMHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LXUONZRYX4PW4D4OPFONFJWMHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LXUONZRYX4PW4D4OPFONFJWMHP/action/storage_attestation","attest_author":"https://pith.science/pith/LXUONZRYX4PW4D4OPFONFJWMHP/action/author_attestation","sign_citation":"https://pith.science/pith/LXUONZRYX4PW4D4OPFONFJWMHP/action/citation_signature","submit_replication":"https://pith.science/pith/LXUONZRYX4PW4D4OPFONFJWMHP/action/replication_record"}},"created_at":"2026-05-18T02:42:39.814278+00:00","updated_at":"2026-05-18T02:42:39.814278+00:00"}