{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7OXWPWC33ZIPHSOYCFMJ4V3IEY","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":"aec7d1923787822a00c23576d1e1c2b4631e3fd5a80af8b7e05644d13bdb1f04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-08T14:35:31Z","title_canon_sha256":"c430a0825d5e49d925bc13da082db38e08d73d3b5ec3f9220386c69dce1a8c95"},"schema_version":"1.0","source":{"id":"1501.01869","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01869","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01869v6","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01869","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"7OXWPWC33ZIP","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7OXWPWC33ZIPHSOY","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7OXWPWC3","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:4649e65e0b548d1a51cefb8624c9e0c7b2a277d95161e3aedf3dbed79a7e6d0f","target":"graph","created_at":"2026-05-18T00:22:40Z","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":"Consider a sequence of continuous-time irreducible reversible Markov chains and a sequence of initial distributions, $\\mu_n$. The sequence is said to exhibit $\\mu_n$-cutoff if the convergence to stationarity in total variation distance is abrupt, w.r.t. this sequence of initial distributions.\n  In this work we give a characterization of $\\mu_n$-cutoff for an arbitrary sequence of initial distributions $\\mu_n$ (in the above setup). Our characterization is expressed in terms of hitting times of sets which are \"worst\" w.r.t. $\\mu_n$.\n  Consider a Markov chain on $\\Omega$ whose stationary distribu","authors_text":"Jonathan Hermon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-08T14:35:31Z","title":"A technical report on hitting times, mixing and cutoff"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01869","kind":"arxiv","version":6},"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":"sha256:9a3f1104d4cc7e15b234d84597a79a346747fdcbf30e1da9aec88a8a4f232528","target":"record","created_at":"2026-05-18T00:22:40Z","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":"aec7d1923787822a00c23576d1e1c2b4631e3fd5a80af8b7e05644d13bdb1f04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-08T14:35:31Z","title_canon_sha256":"c430a0825d5e49d925bc13da082db38e08d73d3b5ec3f9220386c69dce1a8c95"},"schema_version":"1.0","source":{"id":"1501.01869","kind":"arxiv","version":6}},"canonical_sha256":"fbaf67d85bde50f3c9d811589e5768263966fe8476a34e0e8c0b154fdbb00fdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbaf67d85bde50f3c9d811589e5768263966fe8476a34e0e8c0b154fdbb00fdf","first_computed_at":"2026-05-18T00:22:40.625228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:40.625228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D7VINvk8RkcFv12bXO4PhEzrIR/NbrmuzkVfr6clYFNBJrbY8+qBg1fmy7WrNIHd64mFNVJNUwUnt2HMR9ofAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:40.625812Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01869","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a3f1104d4cc7e15b234d84597a79a346747fdcbf30e1da9aec88a8a4f232528","sha256:4649e65e0b548d1a51cefb8624c9e0c7b2a277d95161e3aedf3dbed79a7e6d0f"],"state_sha256":"908a4fe3bab0b480f8a58d951127cb3abb2ad007e4fa15b342f17b0627434835"}