{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DDRDHCQYZFXIE5IIWFSSMS7AVV","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":"32a024238ab2af20821d85d0aa11588f5980a02ee635d1e690d864b904ae00a9","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-22T17:49:47Z","title_canon_sha256":"5de3f8639dd25e5b1e8896996f382d765fa98ebf47d7efdf8a3543f8275c1dbf"},"schema_version":"1.0","source":{"id":"1505.06161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06161","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06161v1","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06161","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"pith_short_12","alias_value":"DDRDHCQYZFXI","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DDRDHCQYZFXIE5II","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DDRDHCQY","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:6e4b6a032591d046471063a5085072ca9107b832cd91fd94c5a41986f04a42fd","target":"graph","created_at":"2026-05-18T02:03:48Z","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 consider random lattice triangulations of $n\\times k$ rectangular regions with weight $\\lambda^{|\\sigma|}$ where $\\lambda>0$ is a parameter and $|\\sigma|$ denotes the total edge length of the triangulation. When $\\lambda\\in(0,1)$ and $k$ is fixed, we prove a tight upper bound of order $n^2$ for the mixing time of the edge-flip Glauber dynamics. Combined with the previously known lower bound of order $\\exp(\\Omega(n^2))$ for $\\lambda>1$ [3], this establishes the existence of a dynamical phase transition for thin rectangles with critical point at $\\lambda=1$.","authors_text":"Alexandre Stauffer, Alistair Sinclair, Fabio Martinelli, Pietro Caputo","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-22T17:49:47Z","title":"Dynamics of Lattice Triangulations on Thin Rectangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06161","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:e96ffd6f615594b8f9aad7158b8f33e5d2f3f3b8fa74be9ac505f0e8fb539331","target":"record","created_at":"2026-05-18T02:03:48Z","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":"32a024238ab2af20821d85d0aa11588f5980a02ee635d1e690d864b904ae00a9","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-22T17:49:47Z","title_canon_sha256":"5de3f8639dd25e5b1e8896996f382d765fa98ebf47d7efdf8a3543f8275c1dbf"},"schema_version":"1.0","source":{"id":"1505.06161","kind":"arxiv","version":1}},"canonical_sha256":"18e2338a18c96e827508b165264be0ad5a11bad80c8f7e5b4168da2c91f9274f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18e2338a18c96e827508b165264be0ad5a11bad80c8f7e5b4168da2c91f9274f","first_computed_at":"2026-05-18T02:03:48.883233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:48.883233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+eRD/4xbLc/se0jrsUzY+ZvXzJbZOegk8pgesC4RhXLTupI2N1GAJleiAySjMXQYIgPH5fJCmVVP+k22yR6CAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:48.883996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e96ffd6f615594b8f9aad7158b8f33e5d2f3f3b8fa74be9ac505f0e8fb539331","sha256:6e4b6a032591d046471063a5085072ca9107b832cd91fd94c5a41986f04a42fd"],"state_sha256":"6932ad8cae828448de09fecd60509a5dc34e286a6a9e1d2c4c3ee881c320787f"}