{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:6QTO73Q5RQTDI2XGYGKXP7AWQN","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":"63cc8d4c702b3aedda36cd7ae28abb4172cda101cac3c6003a81a4a369c91b48","cross_cats_sorted":["cs.CG","cs.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2006-08-12T23:31:07Z","title_canon_sha256":"07526509ddc540435d9918bd6a39323f53cdf093d02bd67e0b9871216d69d2b9"},"schema_version":"1.0","source":{"id":"cs/0608054","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0608054","created_at":"2026-07-04T15:12:14Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0608054v2","created_at":"2026-07-04T15:12:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0608054","created_at":"2026-07-04T15:12:14Z"},{"alias_kind":"pith_short_12","alias_value":"6QTO73Q5RQTD","created_at":"2026-07-04T15:12:14Z"},{"alias_kind":"pith_short_16","alias_value":"6QTO73Q5RQTDI2XG","created_at":"2026-07-04T15:12:14Z"},{"alias_kind":"pith_short_8","alias_value":"6QTO73Q5","created_at":"2026-07-04T15:12:14Z"}],"graph_snapshots":[{"event_id":"sha256:cb36a84a858e50d36f25a334517bdd7153dae7cd061e708cd7ad3e7601ce5ada","target":"graph","created_at":"2026-07-04T15:12:14Z","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/cs/0608054/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"How much can randomness help computation? Motivated by this general question and by volume computation, one of the few instances where randomness provably helps, we analyze a notion of dispersion and connect it to asymptotic convex geometry. We obtain a nearly quadratic lower bound on the complexity of randomized volume algorithms for convex bodies in R^n (the current best algorithm has complexity roughly n^4, conjectured to be n^3). Our main tools, dispersion of random determinants and dispersion of the length of a random point from a convex body, are of independent interest and applicable mo","authors_text":"Luis Rademacher, Santosh Vempala","cross_cats":["cs.CG","cs.DS","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2006-08-12T23:31:07Z","title":"Dispersion of Mass and the Complexity of Randomized Geometric Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0608054","kind":"arxiv","version":2},"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:c232948355e6be8a10f784d7f39eaa725082a2f308fcd6afe53f07272e178d68","target":"record","created_at":"2026-07-04T15:12:14Z","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":"63cc8d4c702b3aedda36cd7ae28abb4172cda101cac3c6003a81a4a369c91b48","cross_cats_sorted":["cs.CG","cs.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2006-08-12T23:31:07Z","title_canon_sha256":"07526509ddc540435d9918bd6a39323f53cdf093d02bd67e0b9871216d69d2b9"},"schema_version":"1.0","source":{"id":"cs/0608054","kind":"arxiv","version":2}},"canonical_sha256":"f426efee1d8c26346ae6c19577fc16836687aab8920e42118eb2a2e8b06a2680","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f426efee1d8c26346ae6c19577fc16836687aab8920e42118eb2a2e8b06a2680","first_computed_at":"2026-07-04T15:12:14.941629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:12:14.941629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kxli5LGcGJXJTFyhx/CJ+QESl4QZJ2lIhD0j8Svu3mIoNovoSSNpeYcPBLcBMnw+rx/d5vhzrViaFqzGQ132Ag==","signature_status":"signed_v1","signed_at":"2026-07-04T15:12:14.942046Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0608054","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c232948355e6be8a10f784d7f39eaa725082a2f308fcd6afe53f07272e178d68","sha256:cb36a84a858e50d36f25a334517bdd7153dae7cd061e708cd7ad3e7601ce5ada"],"state_sha256":"4c249767870854b245f6aaef802f6000ad0e6cf4a4857a63c8aff41eb42a7504"}