{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NFRGLFXH3AZP5X6GOCIN2RZXRR","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":"0b4d7cb263db53848aa3c4f0ef5708e35b534c2856cfcd5855a8ce019f314e6e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-26T07:25:27Z","title_canon_sha256":"0298ffde55d0f613ea886a38b417c802551eb11722f25708904b33a1a275f94c"},"schema_version":"1.0","source":{"id":"1312.7061","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7061","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7061v2","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7061","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"NFRGLFXH3AZP","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NFRGLFXH3AZP5X6G","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NFRGLFXH","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:0264f59714ea491aa89e84555b0fad3e797876f2ff50b809f548c5be28b589e1","target":"graph","created_at":"2026-05-17T23:52:44Z","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"},"paper":{"abstract_excerpt":"We introduce the concept of accessibility and prove that any convex body $X$ in $\\mathbb R^d$ is accessible with relevant constants depending on $d$ only. This property leads to a new algorithm which may be considered as a natural derandomization of the hit and run algorithm applied to generate a sequence of random points covering $X$ uniformly. We prove stability of the Markov chain generated by the proposed algorithm and provide its rate of convergence.","authors_text":"Benoit Collins, Karol \\.Zyczkowski, Rafa{\\l} Kulik, Termeh Kousha, Tomasz Szarek","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-26T07:25:27Z","title":"The accessibility of convex bodies and derandomization of the hit and run algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7061","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":"sha256:3491a525d2367929fc44e8bccb93e0fefaae2ca3b1d81930dc19cd5640d93bf2","target":"record","created_at":"2026-05-17T23:52:44Z","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":"0b4d7cb263db53848aa3c4f0ef5708e35b534c2856cfcd5855a8ce019f314e6e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-26T07:25:27Z","title_canon_sha256":"0298ffde55d0f613ea886a38b417c802551eb11722f25708904b33a1a275f94c"},"schema_version":"1.0","source":{"id":"1312.7061","kind":"arxiv","version":2}},"canonical_sha256":"69626596e7d832fedfc67090dd47378c6e327c18d3c59dd42e14e43e45d2c1fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69626596e7d832fedfc67090dd47378c6e327c18d3c59dd42e14e43e45d2c1fe","first_computed_at":"2026-05-17T23:52:44.893979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:44.893979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VNCNTxQ0DrbeNP70oQTItOYIE2XwvaaxNDgpscmeOj8G6X1BuXm2UrLy/HSdmMlcwGsqPMLl6lo2iyPmE74HBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:44.894509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7061","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3491a525d2367929fc44e8bccb93e0fefaae2ca3b1d81930dc19cd5640d93bf2","sha256:0264f59714ea491aa89e84555b0fad3e797876f2ff50b809f548c5be28b589e1"],"state_sha256":"f8aef50fc1da15a5daec0b2c745d0fff2e920278398fa0b05c6eab16e2510af4"}