{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:EXP73ZBJ7M7DE7QKA4SUEZVZZ3","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":"ccdb3ea60b57d9f581d2b9582c30d7a245e943bcd5244d3ae394b2d0aa2ff95a","cross_cats_sorted":["cs.CC","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-08-05T14:08:16Z","title_canon_sha256":"89eee9eee98474360374b612923ab38b6e8a894b3b60ebf5d44038fb0e791ed4"},"schema_version":"1.0","source":{"id":"2008.02146","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.02146","created_at":"2026-07-05T09:00:33Z"},{"alias_kind":"arxiv_version","alias_value":"2008.02146v3","created_at":"2026-07-05T09:00:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.02146","created_at":"2026-07-05T09:00:33Z"},{"alias_kind":"pith_short_12","alias_value":"EXP73ZBJ7M7D","created_at":"2026-07-05T09:00:33Z"},{"alias_kind":"pith_short_16","alias_value":"EXP73ZBJ7M7DE7QK","created_at":"2026-07-05T09:00:33Z"},{"alias_kind":"pith_short_8","alias_value":"EXP73ZBJ","created_at":"2026-07-05T09:00:33Z"}],"graph_snapshots":[{"event_id":"sha256:4a20a84ad3ef0a774545b49e80c61a8b957bddbf804f458b69d3820e2476b18b","target":"graph","created_at":"2026-07-05T09:00:33Z","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/2008.02146/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the volume of a convex body in $\\mathbb{R}^{n}$ in the general membership oracle model can be computed to within relative error $\\varepsilon$ using $\\widetilde{O}(n^{3.5}\\psi^{2} + n^3/\\varepsilon^{2})$ oracle queries, where $\\psi$ is the KLS constant. With the current bound of $\\psi=\\widetilde{O}(1)$, this gives an $\\widetilde{O}(n^{3.5} + n^3/\\varepsilon^{2})$ algorithm, improving on the Lov\\'{a}sz-Vempala $\\widetilde{O}(n^{4}/\\varepsilon^{2})$ algorithm from 2003. The main new ingredient is an $\\widetilde{O}(n^{3}\\psi^{2})$ algorithm for isotropic transformation of a well-round","authors_text":"Aditi Laddha, He Jia, Santosh S. Vempala, Yin Tat Lee","cross_cats":["cs.CC","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-08-05T14:08:16Z","title":"Reducing Isotropy and Volume to KLS: Faster Rounding and Volume Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.02146","kind":"arxiv","version":3},"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":"sha256:153948b3a626ea056c07e19a7c98247fe41f49ae6741df94022ef052eefdb8ad","target":"record","created_at":"2026-07-05T09:00:33Z","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":"ccdb3ea60b57d9f581d2b9582c30d7a245e943bcd5244d3ae394b2d0aa2ff95a","cross_cats_sorted":["cs.CC","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-08-05T14:08:16Z","title_canon_sha256":"89eee9eee98474360374b612923ab38b6e8a894b3b60ebf5d44038fb0e791ed4"},"schema_version":"1.0","source":{"id":"2008.02146","kind":"arxiv","version":3}},"canonical_sha256":"25dffde429fb3e327e0a07254266b9cef3ce080977834192f8a5a565055cf831","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25dffde429fb3e327e0a07254266b9cef3ce080977834192f8a5a565055cf831","first_computed_at":"2026-07-05T09:00:33.765580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:00:33.765580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tErZu2jMRkpJ0MNCCVbWiloq3nN56xo3MNGeYmiYw5qlq2qqR1JMAFQsFMrtiGlZsbLnSOYR4QdniYEW7ge1Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:00:33.766128Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.02146","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:153948b3a626ea056c07e19a7c98247fe41f49ae6741df94022ef052eefdb8ad","sha256:4a20a84ad3ef0a774545b49e80c61a8b957bddbf804f458b69d3820e2476b18b"],"state_sha256":"3fe08d4bed7cb4abde692352be81e2bba05216777c2c151380241cdd5b47a4e7"}