{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BOBCKLKQUMULME6VB6HM45F5BF","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":"39234b6988d9d93c1d886e71ae61c33475662a5dff72b8fd5b6cfb37b8df1acf","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-13T17:15:31Z","title_canon_sha256":"ec3fcabba7fdc0c7b3051a1936cc238bef5b9472019140c5625e39911b63ba2d"},"schema_version":"1.0","source":{"id":"2608.13487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13487","created_at":"2026-08-14T01:24:51Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13487v1","created_at":"2026-08-14T01:24:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13487","created_at":"2026-08-14T01:24:51Z"},{"alias_kind":"pith_short_12","alias_value":"BOBCKLKQUMUL","created_at":"2026-08-14T01:24:51Z"},{"alias_kind":"pith_short_16","alias_value":"BOBCKLKQUMULME6V","created_at":"2026-08-14T01:24:51Z"},{"alias_kind":"pith_short_8","alias_value":"BOBCKLKQ","created_at":"2026-08-14T01:24:51Z"}],"graph_snapshots":[{"event_id":"sha256:49a786f47ed9624e3d1e16c924937b62c77226505fedca8a952936974641a573","target":"graph","created_at":"2026-08-14T01:24:51Z","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/2608.13487/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $K\\subset\\mathbb{R}^n$ be an isotropic convex body. We prove that the hit-and-run walk, started from any $M$-warm distribution, reaches total-variation distance $\\varepsilon$ from the uniform distribution on $K$ in $O\\!\\left(n^2\\psi_n^{-2}\\log^3(M/\\varepsilon)\\right)$ steps, where $\\psi_n^{-1}$ is the Kannan-Lov\\'asz-Simonovits (KLS) constant. Up to logarithmic factors, this matches the best-known warm-start mixing time for the ball walk. Chen and Eldan [Discrete Comput. Geom. 2026] obtained the same $n^2\\psi_n^{-2}$ dependence for hit-and-run, but with polynomial dependence on $M/\\varepsi","authors_text":"Ruizhe Zhang","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-13T17:15:31Z","title":"Hit-and-Run Mixes as Fast as the Ball Walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13487","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:b7fcbfdb0bb95e4df95598f287a7a2665f1d1bdd8d540731bc4bf89d36f5b311","target":"record","created_at":"2026-08-14T01:24:51Z","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":"39234b6988d9d93c1d886e71ae61c33475662a5dff72b8fd5b6cfb37b8df1acf","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-13T17:15:31Z","title_canon_sha256":"ec3fcabba7fdc0c7b3051a1936cc238bef5b9472019140c5625e39911b63ba2d"},"schema_version":"1.0","source":{"id":"2608.13487","kind":"arxiv","version":1}},"canonical_sha256":"0b82252d50a328b613d50f8ece74bd095b6b358c56fba9e3f7775b8fc1a0d729","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b82252d50a328b613d50f8ece74bd095b6b358c56fba9e3f7775b8fc1a0d729","first_computed_at":"2026-08-14T01:24:51.178327Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-14T01:24:51.178327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uTDGG5KQrYsHzHVJMStTG8lrCiWaU2MxzlKcVPQdVSbYaKre0+qxwb7UN9ZqTfRHEr0MJSKuBErexqf7eokOAg==","signature_status":"signed_v1","signed_at":"2026-08-14T01:24:51.180554Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.13487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7fcbfdb0bb95e4df95598f287a7a2665f1d1bdd8d540731bc4bf89d36f5b311","sha256:49a786f47ed9624e3d1e16c924937b62c77226505fedca8a952936974641a573"],"state_sha256":"e04026136cea90751d07a814f02d9eb4b3b1df72213d0b965b2a10d4831b36c8"}