{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TKP3VLINP47SSDWKBZEWYZGSVH","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":"fbfe81ded7a7305307145048ab5cb14a9a16b4892969be8d5532cfc27841820d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-09-07T22:42:52Z","title_canon_sha256":"155c97edf581739aa84dd8d7473a1566ad5796194d47acc7506a38d1470f098c"},"schema_version":"1.0","source":{"id":"1809.02703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02703","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02703v1","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02703","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"TKP3VLINP47S","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TKP3VLINP47SSDWK","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TKP3VLIN","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:f5f6aefac427d24e5386c6ccb947c01f53cff24ebe3c4a6ec2c6a73e37ca98f9","target":"graph","created_at":"2026-05-18T00:06:15Z","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":"In this paper, we study the mixing time of two widely used Markov chain algorithms for the six-vertex model, Glauber dynamics and the directed-loop algorithm, on the square lattice $\\mathbb{Z}^2$. We prove, for the first time that, on finite regions of the square lattice these Markov chains are torpidly mixing under parameter settings in the ferroelectric phase and the anti-ferroelectric phase.","authors_text":"Tianyu Liu","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-09-07T22:42:52Z","title":"Torpid Mixing of Markov Chains for the Six-vertex Model on $\\mathbb{Z}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02703","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:bfa6c8e334c6a1c3d3cade6176a9f525c0a1249cff2838869656a6131683e972","target":"record","created_at":"2026-05-18T00:06:15Z","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":"fbfe81ded7a7305307145048ab5cb14a9a16b4892969be8d5532cfc27841820d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-09-07T22:42:52Z","title_canon_sha256":"155c97edf581739aa84dd8d7473a1566ad5796194d47acc7506a38d1470f098c"},"schema_version":"1.0","source":{"id":"1809.02703","kind":"arxiv","version":1}},"canonical_sha256":"9a9fbaad0d7f3f290eca0e496c64d2a9c47aec22b16daccf2623621fbabacf21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a9fbaad0d7f3f290eca0e496c64d2a9c47aec22b16daccf2623621fbabacf21","first_computed_at":"2026-05-18T00:06:15.566673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:15.566673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9aEyO9jtlNj7vF9KRhTcBMdt0DOC1MzuftsLJbbpP18iGa6mYGrZOhyDMAjpcGjU1Tgao6gU/3iID50Y31RZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:15.567176Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfa6c8e334c6a1c3d3cade6176a9f525c0a1249cff2838869656a6131683e972","sha256:f5f6aefac427d24e5386c6ccb947c01f53cff24ebe3c4a6ec2c6a73e37ca98f9"],"state_sha256":"5fce61e1c168accb651dd865205591e2889c34a8db5ab9811278293c830b7789"}