{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4IZMDAFXGBVNFNUH4G22LA73P2","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":"469dc25cd37be13fec897553cafd382a9beb7eaa3bed6032b2a2e2252078c717","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-24T21:00:05Z","title_canon_sha256":"ad943e05bc24ad38cc391ef9aa60ae9694c6142364fa6992f153e36565a853a7"},"schema_version":"1.0","source":{"id":"1511.07877","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07877","created_at":"2026-05-18T00:36:41Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07877v3","created_at":"2026-05-18T00:36:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07877","created_at":"2026-05-18T00:36:41Z"},{"alias_kind":"pith_short_12","alias_value":"4IZMDAFXGBVN","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4IZMDAFXGBVNFNUH","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4IZMDAFX","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:9b77e465f4e7b7a3b428fdbb0271d9329f72067a40c65b6ca7afe6e10a18edf7","target":"graph","created_at":"2026-05-18T00:36:41Z","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 for the 3-state Potts antiferromagnet at low temperature on $\\mathbb{Z}^d$ for sufficiently large $d$. In particular, we show the existence of six extremal and ergodic infinite-volume Gibbs measures, which exhibit spontaneous magnetization in the sense that vertices in one bipartition class have a much higher probability to be in one state than in either of the other two states. This settles the high-dimensional case of the Koteck\\'y conjecture.","authors_text":"Ohad Feldheim, Yinon Spinka","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-24T21:00:05Z","title":"Long-range order in the 3-state antiferromagnetic Potts model in high dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07877","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":"sha256:4504c99a52e8d3630ccab19207accaf804421f15c794c8ad09ad831dca6ec69d","target":"record","created_at":"2026-05-18T00:36:41Z","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":"469dc25cd37be13fec897553cafd382a9beb7eaa3bed6032b2a2e2252078c717","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-24T21:00:05Z","title_canon_sha256":"ad943e05bc24ad38cc391ef9aa60ae9694c6142364fa6992f153e36565a853a7"},"schema_version":"1.0","source":{"id":"1511.07877","kind":"arxiv","version":3}},"canonical_sha256":"e232c180b7306ad2b687e1b5a583fb7ea4ce36a13916a9991e0438fa312a9640","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e232c180b7306ad2b687e1b5a583fb7ea4ce36a13916a9991e0438fa312a9640","first_computed_at":"2026-05-18T00:36:41.554138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:41.554138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WoMX7GIVv3BQ94TSA9rZXQlemFpHskf6wH4F/0KHQUVmt8OFc+uZlHjPKHSQKKhwgEJYfpV9jTwtRmcKyYhaBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:41.554816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07877","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4504c99a52e8d3630ccab19207accaf804421f15c794c8ad09ad831dca6ec69d","sha256:9b77e465f4e7b7a3b428fdbb0271d9329f72067a40c65b6ca7afe6e10a18edf7"],"state_sha256":"dc4fe9e435e185843f73fc05f4f5081779539f147947cce860fb3602bf65eb03"}