{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:HNMPBV2WP25G7SRWJASLV27EM5","short_pith_number":"pith:HNMPBV2W","canonical_record":{"source":{"id":"0805.3587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-05-23T07:08:28Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"2cb7fcfce93bf7be327325f6bfca4749c1ae0361533dd4e60d924013dbcd2750","abstract_canon_sha256":"79e66c143a36f78d285f094ad98363b227f467439e1786056d08ff5ad9082ea9"},"schema_version":"1.0"},"canonical_sha256":"3b58f0d7567eba6fca364824baebe4676a54dfde9a2f7f9a535e8b2e3c2e24b7","source":{"kind":"arxiv","id":"0805.3587","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.3587","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"0805.3587v2","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.3587","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"HNMPBV2WP25G","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"HNMPBV2WP25G7SRW","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"HNMPBV2W","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:HNMPBV2WP25G7SRWJASLV27EM5","target":"record","payload":{"canonical_record":{"source":{"id":"0805.3587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-05-23T07:08:28Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"2cb7fcfce93bf7be327325f6bfca4749c1ae0361533dd4e60d924013dbcd2750","abstract_canon_sha256":"79e66c143a36f78d285f094ad98363b227f467439e1786056d08ff5ad9082ea9"},"schema_version":"1.0"},"canonical_sha256":"3b58f0d7567eba6fca364824baebe4676a54dfde9a2f7f9a535e8b2e3c2e24b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:31.467378Z","signature_b64":"+TZqO0gCBbMj77PeOGyqNLU5wmQRGMDTRGrlOdCJMV2TzV5pkJnNQ+P92ftIYcLtxTg41826MhanmcitmOujDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b58f0d7567eba6fca364824baebe4676a54dfde9a2f7f9a535e8b2e3c2e24b7","last_reissued_at":"2026-05-18T04:31:31.466805Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:31.466805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0805.3587","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3hqrUxiOXCFXCLhG3kVFzJPZPsrMhYX8W/Hn62PmFZdm2iPOc2Y9AfGZCxAookjTR1naOSluSR4FRTc8uiRDDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:43:53.466120Z"},"content_sha256":"bb5d84ea40c6912b0d7bed1a7a8bc0923d9fe08aa14dec07096526a0b812417f","schema_version":"1.0","event_id":"sha256:bb5d84ea40c6912b0d7bed1a7a8bc0923d9fe08aa14dec07096526a0b812417f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:HNMPBV2WP25G7SRWJASLV27EM5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit error bounds for lazy reversible Markov Chain Monte Carlo","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NA","authors_text":"Daniel Rudolf","submitted_at":"2008-05-23T07:08:28Z","abstract_excerpt":"We prove explicit, i.e., non-asymptotic, error bounds for Markov Chain Monte Carlo methods, such as the Metropolis algorithm. The problem is to compute the expectation (or integral) of f with respect to a measure which can be given by a density with respect to another measure. A straight simulation of the desired distribution by a random number generator is in general not possible. Thus it is reasonable to use Markov chain sampling with a burn-in. We study such an algorithm and extend the analysis of Lovasz and Simonovits (1993) to obtain an explicit error bound."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.3587","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kKx7ZpxC40asIdgFIv7eGKLf5KoTV1kA9OX38VEokVi5ezu6UgSQjOM9pwYP6FkyjpZiE8eLLX3+PRRz543qBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:43:53.466482Z"},"content_sha256":"f2dec02cad5f2d04366caf9e9185cedf4b7aa256d20c0d6249a49a47ea5ef998","schema_version":"1.0","event_id":"sha256:f2dec02cad5f2d04366caf9e9185cedf4b7aa256d20c0d6249a49a47ea5ef998"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNMPBV2WP25G7SRWJASLV27EM5/bundle.json","state_url":"https://pith.science/pith/HNMPBV2WP25G7SRWJASLV27EM5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNMPBV2WP25G7SRWJASLV27EM5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T05:43:53Z","links":{"resolver":"https://pith.science/pith/HNMPBV2WP25G7SRWJASLV27EM5","bundle":"https://pith.science/pith/HNMPBV2WP25G7SRWJASLV27EM5/bundle.json","state":"https://pith.science/pith/HNMPBV2WP25G7SRWJASLV27EM5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNMPBV2WP25G7SRWJASLV27EM5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:HNMPBV2WP25G7SRWJASLV27EM5","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":"79e66c143a36f78d285f094ad98363b227f467439e1786056d08ff5ad9082ea9","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-05-23T07:08:28Z","title_canon_sha256":"2cb7fcfce93bf7be327325f6bfca4749c1ae0361533dd4e60d924013dbcd2750"},"schema_version":"1.0","source":{"id":"0805.3587","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.3587","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"0805.3587v2","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.3587","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"HNMPBV2WP25G","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"HNMPBV2WP25G7SRW","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"HNMPBV2W","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:f2dec02cad5f2d04366caf9e9185cedf4b7aa256d20c0d6249a49a47ea5ef998","target":"graph","created_at":"2026-05-18T04:31:31Z","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 prove explicit, i.e., non-asymptotic, error bounds for Markov Chain Monte Carlo methods, such as the Metropolis algorithm. The problem is to compute the expectation (or integral) of f with respect to a measure which can be given by a density with respect to another measure. A straight simulation of the desired distribution by a random number generator is in general not possible. Thus it is reasonable to use Markov chain sampling with a burn-in. We study such an algorithm and extend the analysis of Lovasz and Simonovits (1993) to obtain an explicit error bound.","authors_text":"Daniel Rudolf","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-05-23T07:08:28Z","title":"Explicit error bounds for lazy reversible Markov Chain Monte Carlo"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.3587","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:bb5d84ea40c6912b0d7bed1a7a8bc0923d9fe08aa14dec07096526a0b812417f","target":"record","created_at":"2026-05-18T04:31:31Z","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":"79e66c143a36f78d285f094ad98363b227f467439e1786056d08ff5ad9082ea9","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-05-23T07:08:28Z","title_canon_sha256":"2cb7fcfce93bf7be327325f6bfca4749c1ae0361533dd4e60d924013dbcd2750"},"schema_version":"1.0","source":{"id":"0805.3587","kind":"arxiv","version":2}},"canonical_sha256":"3b58f0d7567eba6fca364824baebe4676a54dfde9a2f7f9a535e8b2e3c2e24b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b58f0d7567eba6fca364824baebe4676a54dfde9a2f7f9a535e8b2e3c2e24b7","first_computed_at":"2026-05-18T04:31:31.466805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:31.466805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+TZqO0gCBbMj77PeOGyqNLU5wmQRGMDTRGrlOdCJMV2TzV5pkJnNQ+P92ftIYcLtxTg41826MhanmcitmOujDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:31.467378Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.3587","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb5d84ea40c6912b0d7bed1a7a8bc0923d9fe08aa14dec07096526a0b812417f","sha256:f2dec02cad5f2d04366caf9e9185cedf4b7aa256d20c0d6249a49a47ea5ef998"],"state_sha256":"2347011db1908df6e316178ffccc925e16abbf8f7ff13dbe169a2d5159b693f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u8fRGpz9+dOqftwDB8eEG3USBm7SsPHGd/WQ9p1ApOrWF7QBsL/HtQpTglfeYSbNSra8Oqzai99RBMK9yvp0DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:43:53.468551Z","bundle_sha256":"b73a47d61501daed8110bb7537ff329cf969e14cce7deff51fda0f4e2e1f3952"}}