{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5QIRYOIDDLUZ7OOHZAWQNJZFHR","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":"09eb3c90cacb0525a1b338b4774c29f6b8cc6080a1151ba1601932f915caa3c0","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-28T20:53:00Z","title_canon_sha256":"f89dd659984124881567b4d4555a050cb4d3866cdde003e9b05bf625eb79375b"},"schema_version":"1.0","source":{"id":"1107.5829","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5829","created_at":"2026-05-18T03:02:18Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5829v2","created_at":"2026-05-18T03:02:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5829","created_at":"2026-05-18T03:02:18Z"},{"alias_kind":"pith_short_12","alias_value":"5QIRYOIDDLUZ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5QIRYOIDDLUZ7OOH","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5QIRYOID","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:68d26ede0b065960fdf5afbc3326bc0525dfbd7b60aa0bf161a4264d22e9b5e2","target":"graph","created_at":"2026-05-18T03:02:18Z","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 determine the mixing time of a simple Gibbs sampler on the unit simplex, confirming a conjecture of Aldous. The upper bound is based on a two-step coupling, where the first step is a simple contraction argument and the second step is a non-Markovian coupling. We also present a MCMC-based perfect sampling algorithm based on our proof which can be applied with Gibbs samplers that are harder to analyze.","authors_text":"Aaron Smith","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-28T20:53:00Z","title":"A Gibbs sampler on the $n$-simplex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5829","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":"sha256:801f87f025739c2b47b9b57decc144aac0729bfdd4e88b86d0d0ec5fe13d45d3","target":"record","created_at":"2026-05-18T03:02:18Z","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":"09eb3c90cacb0525a1b338b4774c29f6b8cc6080a1151ba1601932f915caa3c0","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-28T20:53:00Z","title_canon_sha256":"f89dd659984124881567b4d4555a050cb4d3866cdde003e9b05bf625eb79375b"},"schema_version":"1.0","source":{"id":"1107.5829","kind":"arxiv","version":2}},"canonical_sha256":"ec111c39031ae99fb9c7c82d06a7253c7ee49d4655833d4d40adfefd8a1b4835","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec111c39031ae99fb9c7c82d06a7253c7ee49d4655833d4d40adfefd8a1b4835","first_computed_at":"2026-05-18T03:02:18.203696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:18.203696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qCwZyPNoAUr4ZbRw7cXYAkzQGkqbo/NSscfzXkcbX2Z6k/DTxUPAiT428TaAh/p3DEozH+T54QspudtT0skpBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:18.204491Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5829","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:801f87f025739c2b47b9b57decc144aac0729bfdd4e88b86d0d0ec5fe13d45d3","sha256:68d26ede0b065960fdf5afbc3326bc0525dfbd7b60aa0bf161a4264d22e9b5e2"],"state_sha256":"e38acbeedeb6f55f7ccf01d22665092be9d01f978dfb6e195960a049c03ac8cf"}