{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:ZP52L63QK7BX6OFPH7FKHODG42","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":"ffd1ac158c27d35ae4ba32fdbdc76d16e7e7da5322735fa9f2405b610c3d81e2","cross_cats_sorted":["cs.CC","stat.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-12-01T06:06:52Z","title_canon_sha256":"b7fd0050dc26f3e6ab1aff9d9c3a59a24793b0e427df04f6c5323f44728a5f98"},"schema_version":"1.0","source":{"id":"2212.00297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.00297","created_at":"2026-07-05T05:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"2212.00297v1","created_at":"2026-07-05T05:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.00297","created_at":"2026-07-05T05:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"ZP52L63QK7BX","created_at":"2026-07-05T05:21:32Z"},{"alias_kind":"pith_short_16","alias_value":"ZP52L63QK7BX6OFP","created_at":"2026-07-05T05:21:32Z"},{"alias_kind":"pith_short_8","alias_value":"ZP52L63Q","created_at":"2026-07-05T05:21:32Z"}],"graph_snapshots":[{"event_id":"sha256:69284e19c6d178203a23ce4fbf50a4351605fe487688afd9600e601aa8d5ad85","target":"graph","created_at":"2026-07-05T05:21:32Z","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/2212.00297/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze the hit-and-run algorithm for sampling uniformly from an isotropic convex body $K$ in $n$ dimensions. We show that the algorithm mixes in time $\\tilde{O}(n^2/ \\psi_n^2)$, where $\\psi_n$ is the smallest isoperimetric constant for any isotropic logconcave distribution, also known as the Kannan-Lovasz-Simonovits (KLS) constant. Our bound improves upon previous bounds of the form $\\tilde{O}(n^2 R^2/r^2)$, which depend on the ratio $R/r$ of the radii of the circumscribed and inscribed balls of $K$, gaining a factor of $n$ in the case of isotropic convex bodies. Consequently, our result g","authors_text":"Ronen Eldan, Yuansi Chen","cross_cats":["cs.CC","stat.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-12-01T06:06:52Z","title":"Hit-and-run mixing via localization schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.00297","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:f4aba175988c18f4f41175ce893275869c8b4340e63a64c0f7105c67d50908fb","target":"record","created_at":"2026-07-05T05:21:32Z","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":"ffd1ac158c27d35ae4ba32fdbdc76d16e7e7da5322735fa9f2405b610c3d81e2","cross_cats_sorted":["cs.CC","stat.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-12-01T06:06:52Z","title_canon_sha256":"b7fd0050dc26f3e6ab1aff9d9c3a59a24793b0e427df04f6c5323f44728a5f98"},"schema_version":"1.0","source":{"id":"2212.00297","kind":"arxiv","version":1}},"canonical_sha256":"cbfba5fb7057c37f38af3fcaa3b866e6b29630b58ab07370a103e511d0e0d77c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbfba5fb7057c37f38af3fcaa3b866e6b29630b58ab07370a103e511d0e0d77c","first_computed_at":"2026-07-05T05:21:32.927362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:21:32.927362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"208JbKM70BhXBV3hwujLPpYeeeWqIqBoV2xwJIab8WKzbEkh3b7G0oNQ6U168Anlsc028WSbVmsqW49yWAgzAA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:21:32.927821Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.00297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4aba175988c18f4f41175ce893275869c8b4340e63a64c0f7105c67d50908fb","sha256:69284e19c6d178203a23ce4fbf50a4351605fe487688afd9600e601aa8d5ad85"],"state_sha256":"8bd57b2a19478fc162411b9482ba637f2dc937bc2ccfb7764945bc4d9e40956e"}