{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ESS5AKVWC7AE7DLSGY37IRJII5","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":"c18421b6608be674a74a39c6105f95c6c9b95c1b8a3f73bbfb48d2fe8a598429","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-08-28T17:56:09Z","title_canon_sha256":"63b4d4051599d21bf04a0d54548a99edf9d71823969abca68e6de373974f99ed"},"schema_version":"1.0","source":{"id":"2508.21055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.21055","created_at":"2026-07-05T12:01:15Z"},{"alias_kind":"arxiv_version","alias_value":"2508.21055v1","created_at":"2026-07-05T12:01:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.21055","created_at":"2026-07-05T12:01:15Z"},{"alias_kind":"pith_short_12","alias_value":"ESS5AKVWC7AE","created_at":"2026-07-05T12:01:15Z"},{"alias_kind":"pith_short_16","alias_value":"ESS5AKVWC7AE7DLS","created_at":"2026-07-05T12:01:15Z"},{"alias_kind":"pith_short_8","alias_value":"ESS5AKVW","created_at":"2026-07-05T12:01:15Z"}],"graph_snapshots":[{"event_id":"sha256:4b97c0f7a62197c818f243f6735060544dd68e590544f893075c3c0ba2ec27e7","target":"graph","created_at":"2026-07-05T12:01:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.21055/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their distance to equilibrium remains close to its maximal value for a while and suddenly drops to zero as the time parameter reaches a critical threshold. Discovered four decades ago in the context of card shuffling, this surprising phenomenon has since then been observed in a variety of models, from random walks on groups or complex networks to interacting particle ","authors_text":"Justin Salez","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-08-28T17:56:09Z","title":"Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.21055","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:c5551fa9f148ed45326505ddfee0d373049e252fb790a10290036a79381ea1b6","target":"record","created_at":"2026-07-05T12:01:15Z","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":"c18421b6608be674a74a39c6105f95c6c9b95c1b8a3f73bbfb48d2fe8a598429","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-08-28T17:56:09Z","title_canon_sha256":"63b4d4051599d21bf04a0d54548a99edf9d71823969abca68e6de373974f99ed"},"schema_version":"1.0","source":{"id":"2508.21055","kind":"arxiv","version":1}},"canonical_sha256":"24a5d02ab617c04f8d723637f44528477b4dd5f6046f1c2ed1a1ba4235e52e4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24a5d02ab617c04f8d723637f44528477b4dd5f6046f1c2ed1a1ba4235e52e4f","first_computed_at":"2026-07-05T12:01:15.876493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:01:15.876493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7SCIvzm5rMPEpE/dguRJAmTaGVjGXEG/CsGxWCHnrsKlXItXnkik8GKlIfQbxub3/8xw24e+ZxfGjR1sxdzaDA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:01:15.876985Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.21055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5551fa9f148ed45326505ddfee0d373049e252fb790a10290036a79381ea1b6","sha256:4b97c0f7a62197c818f243f6735060544dd68e590544f893075c3c0ba2ec27e7"],"state_sha256":"49953aaf3f634f63e9dfe21b2db015663bb175ee3d5133f0470d3a51f97d3762"}