{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:ZP52L63QK7BX6OFPH7FKHODG42","short_pith_number":"pith:ZP52L63Q","schema_version":"1.0","canonical_sha256":"cbfba5fb7057c37f38af3fcaa3b866e6b29630b58ab07370a103e511d0e0d77c","source":{"kind":"arxiv","id":"2212.00297","version":1},"attestation_state":"computed","paper":{"title":"Hit-and-run mixing via localization schemes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","stat.CO"],"primary_cat":"math.PR","authors_text":"Ronen Eldan, Yuansi Chen","submitted_at":"2022-12-01T06:06:52Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2212.00297","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-12-01T06:06:52Z","cross_cats_sorted":["cs.CC","stat.CO"],"title_canon_sha256":"b7fd0050dc26f3e6ab1aff9d9c3a59a24793b0e427df04f6c5323f44728a5f98","abstract_canon_sha256":"ffd1ac158c27d35ae4ba32fdbdc76d16e7e7da5322735fa9f2405b610c3d81e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:21:32.927821Z","signature_b64":"208JbKM70BhXBV3hwujLPpYeeeWqIqBoV2xwJIab8WKzbEkh3b7G0oNQ6U168Anlsc028WSbVmsqW49yWAgzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbfba5fb7057c37f38af3fcaa3b866e6b29630b58ab07370a103e511d0e0d77c","last_reissued_at":"2026-07-05T05:21:32.927362Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:21:32.927362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hit-and-run mixing via localization schemes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","stat.CO"],"primary_cat":"math.PR","authors_text":"Ronen Eldan, Yuansi Chen","submitted_at":"2022-12-01T06:06:52Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.00297","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.00297/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2212.00297","created_at":"2026-07-05T05:21:32.927420+00:00"},{"alias_kind":"arxiv_version","alias_value":"2212.00297v1","created_at":"2026-07-05T05:21:32.927420+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.00297","created_at":"2026-07-05T05:21:32.927420+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZP52L63QK7BX","created_at":"2026-07-05T05:21:32.927420+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZP52L63QK7BX6OFP","created_at":"2026-07-05T05:21:32.927420+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZP52L63Q","created_at":"2026-07-05T05:21:32.927420+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.12720","citing_title":"Stochastic Localization with Non-Gaussian Tilts and Applications to Tensor Ising Models","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZP52L63QK7BX6OFPH7FKHODG42","json":"https://pith.science/pith/ZP52L63QK7BX6OFPH7FKHODG42.json","graph_json":"https://pith.science/api/pith-number/ZP52L63QK7BX6OFPH7FKHODG42/graph.json","events_json":"https://pith.science/api/pith-number/ZP52L63QK7BX6OFPH7FKHODG42/events.json","paper":"https://pith.science/paper/ZP52L63Q"},"agent_actions":{"view_html":"https://pith.science/pith/ZP52L63QK7BX6OFPH7FKHODG42","download_json":"https://pith.science/pith/ZP52L63QK7BX6OFPH7FKHODG42.json","view_paper":"https://pith.science/paper/ZP52L63Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2212.00297&json=true","fetch_graph":"https://pith.science/api/pith-number/ZP52L63QK7BX6OFPH7FKHODG42/graph.json","fetch_events":"https://pith.science/api/pith-number/ZP52L63QK7BX6OFPH7FKHODG42/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZP52L63QK7BX6OFPH7FKHODG42/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZP52L63QK7BX6OFPH7FKHODG42/action/storage_attestation","attest_author":"https://pith.science/pith/ZP52L63QK7BX6OFPH7FKHODG42/action/author_attestation","sign_citation":"https://pith.science/pith/ZP52L63QK7BX6OFPH7FKHODG42/action/citation_signature","submit_replication":"https://pith.science/pith/ZP52L63QK7BX6OFPH7FKHODG42/action/replication_record"}},"created_at":"2026-07-05T05:21:32.927420+00:00","updated_at":"2026-07-05T05:21:32.927420+00:00"}