{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:2HN225436K4SBS7WT2VIFZDVJ2","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":"71ec1e5181de064b6e5f190464b3f9bee0f502853d235adb745cc94583436822","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-02-10T17:52:33Z","title_canon_sha256":"975ee791eaeae6943daf89211009e0ef06d2c35ea67e132e5b718d5f0ba182a9"},"schema_version":"1.0","source":{"id":"2102.05597","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.05597","created_at":"2026-07-05T02:18:59Z"},{"alias_kind":"arxiv_version","alias_value":"2102.05597v2","created_at":"2026-07-05T02:18:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.05597","created_at":"2026-07-05T02:18:59Z"},{"alias_kind":"pith_short_12","alias_value":"2HN225436K4S","created_at":"2026-07-05T02:18:59Z"},{"alias_kind":"pith_short_16","alias_value":"2HN225436K4SBS7W","created_at":"2026-07-05T02:18:59Z"},{"alias_kind":"pith_short_8","alias_value":"2HN22543","created_at":"2026-07-05T02:18:59Z"}],"graph_snapshots":[{"event_id":"sha256:78d0f04d82b36a641b9abdfae69a11082be76a0ca1c6e103d3370c21bfe548b1","target":"graph","created_at":"2026-07-05T02:18:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.05597/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Discovered in the context of card shuffling by Aldous, Diaconis and Shahshahani, the cutoff phenomenon has since then been established in a variety of Markov chains. However, proving cutoff remains a delicate affair, which requires a detailed knowledge of the chain. Identifying the general mechanisms underlying this phase transition -- without having to pinpoint its precise location -- remains one of the most fundamental open problems in the area of mixing times. In the present paper, we make a step in this direction by establishing cutoff for Markov chains with non-negative curvature, under a","authors_text":"Justin Salez","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-02-10T17:52:33Z","title":"Cutoff for non-negatively curved Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.05597","kind":"arxiv","version":2},"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":"sha256:1ef4158a86609de85223c2bef25afa8ca8d6606be058633408a6b9ee5fbf3b4e","target":"record","created_at":"2026-07-05T02:18:59Z","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":"71ec1e5181de064b6e5f190464b3f9bee0f502853d235adb745cc94583436822","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-02-10T17:52:33Z","title_canon_sha256":"975ee791eaeae6943daf89211009e0ef06d2c35ea67e132e5b718d5f0ba182a9"},"schema_version":"1.0","source":{"id":"2102.05597","kind":"arxiv","version":2}},"canonical_sha256":"d1dbad779bf2b920cbf69eaa82e4754ea541b2a1acb56189ef2c88f213227ee3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1dbad779bf2b920cbf69eaa82e4754ea541b2a1acb56189ef2c88f213227ee3","first_computed_at":"2026-07-05T02:18:59.962662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:18:59.962662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bBnb26pu5XlfuABneOfOZTcldz1uprz8sQ9U9nEbIwq6Jso9kMoUo/C3+u9cT7H8wwoBsbGttCsx8Mkib0TkCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:18:59.963065Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.05597","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ef4158a86609de85223c2bef25afa8ca8d6606be058633408a6b9ee5fbf3b4e","sha256:78d0f04d82b36a641b9abdfae69a11082be76a0ca1c6e103d3370c21bfe548b1"],"state_sha256":"10978aa45db99bab401aa040d77764f632959253d2601ac74dc2d05599c27568"}