{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XF57YNDXGFS52OPD7NNIEVZDAJ","short_pith_number":"pith:XF57YNDX","canonical_record":{"source":{"id":"1108.1708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-08T13:50:42Z","cross_cats_sorted":[],"title_canon_sha256":"320bea8ff9b20aafef1e28bab4d44b35e7aa306d4dfee072f72045f751360c2f","abstract_canon_sha256":"6c45889d9e4212103c3cac83d7290f0032f9dd897d6d0092f4fb78b8a1a0945c"},"schema_version":"1.0"},"canonical_sha256":"b97bfc34773165dd39e3fb5a8257230278f3291d5ef11af7e90f613fea5082cb","source":{"kind":"arxiv","id":"1108.1708","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1708","created_at":"2026-05-18T03:47:01Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1708v2","created_at":"2026-05-18T03:47:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1708","created_at":"2026-05-18T03:47:01Z"},{"alias_kind":"pith_short_12","alias_value":"XF57YNDXGFS5","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XF57YNDXGFS52OPD","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XF57YNDX","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XF57YNDXGFS52OPD7NNIEVZDAJ","target":"record","payload":{"canonical_record":{"source":{"id":"1108.1708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-08T13:50:42Z","cross_cats_sorted":[],"title_canon_sha256":"320bea8ff9b20aafef1e28bab4d44b35e7aa306d4dfee072f72045f751360c2f","abstract_canon_sha256":"6c45889d9e4212103c3cac83d7290f0032f9dd897d6d0092f4fb78b8a1a0945c"},"schema_version":"1.0"},"canonical_sha256":"b97bfc34773165dd39e3fb5a8257230278f3291d5ef11af7e90f613fea5082cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:47:01.408091Z","signature_b64":"N/+bRyAGGjXj/wxrxzVGMUMFlHzTbbFuZ5NJLQuwVsAlKFIF3VQHhLKrbVDO6UnQLmLPsv5U9jaVr0QgSV/rBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b97bfc34773165dd39e3fb5a8257230278f3291d5ef11af7e90f613fea5082cb","last_reissued_at":"2026-05-18T03:47:01.407567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:47:01.407567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.1708","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":"2026-05-18T03:47:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+2Tn3WFeoz/nOqwnuKnPB/E6smnf/5JuHy7bdHjmNj1O0HIP53vwqZx7oUqP3D7MxdKdQ8TmDJOWOTZppwl7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T10:12:20.793844Z"},"content_sha256":"74c3f5c19a3e4602a323da3ddfc59c0088cc83e761fc0fe4a5c7042538c9c803","schema_version":"1.0","event_id":"sha256:74c3f5c19a3e4602a323da3ddfc59c0088cc83e761fc0fe4a5c7042538c9c803"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XF57YNDXGFS52OPD7NNIEVZDAJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixing and hitting times for finite Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Roberto Imbuzeiro Oliveira","submitted_at":"2011-08-08T13:50:42Z","abstract_excerpt":"Let 0<\\alpha<1/2. We show that the mixing time of a continuous-time reversible Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of stationary measure at least \\alpha of the state space. Suitably modified results hold in discrete time and/or without the reversibility assumption. The key technical tool is a construction of a random set A such that the hitting time of A is both light-tailed and a stationary time for the chain. We note that essentially the same results were obtained independently by Peres and Sousi [arXiv:1108.0133]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1708","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":"2026-05-18T03:47:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hqtsLaIKhTBj+mVUTVCz9qRPVQTiWhXwgXVW5anlVt/jPC17+VEfVKv53WedbArBzJpru3siePeNp1QLm0nTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T10:12:20.794343Z"},"content_sha256":"da591c7b236fc923c5c2a7d24f6f4b81156a425d20ff16bb7af19f7601b797f2","schema_version":"1.0","event_id":"sha256:da591c7b236fc923c5c2a7d24f6f4b81156a425d20ff16bb7af19f7601b797f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XF57YNDXGFS52OPD7NNIEVZDAJ/bundle.json","state_url":"https://pith.science/pith/XF57YNDXGFS52OPD7NNIEVZDAJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XF57YNDXGFS52OPD7NNIEVZDAJ/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":"2026-05-24T10:12:20Z","links":{"resolver":"https://pith.science/pith/XF57YNDXGFS52OPD7NNIEVZDAJ","bundle":"https://pith.science/pith/XF57YNDXGFS52OPD7NNIEVZDAJ/bundle.json","state":"https://pith.science/pith/XF57YNDXGFS52OPD7NNIEVZDAJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XF57YNDXGFS52OPD7NNIEVZDAJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XF57YNDXGFS52OPD7NNIEVZDAJ","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":"6c45889d9e4212103c3cac83d7290f0032f9dd897d6d0092f4fb78b8a1a0945c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-08T13:50:42Z","title_canon_sha256":"320bea8ff9b20aafef1e28bab4d44b35e7aa306d4dfee072f72045f751360c2f"},"schema_version":"1.0","source":{"id":"1108.1708","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1708","created_at":"2026-05-18T03:47:01Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1708v2","created_at":"2026-05-18T03:47:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1708","created_at":"2026-05-18T03:47:01Z"},{"alias_kind":"pith_short_12","alias_value":"XF57YNDXGFS5","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XF57YNDXGFS52OPD","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XF57YNDX","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:da591c7b236fc923c5c2a7d24f6f4b81156a425d20ff16bb7af19f7601b797f2","target":"graph","created_at":"2026-05-18T03:47:01Z","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":"Let 0<\\alpha<1/2. We show that the mixing time of a continuous-time reversible Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of stationary measure at least \\alpha of the state space. Suitably modified results hold in discrete time and/or without the reversibility assumption. The key technical tool is a construction of a random set A such that the hitting time of A is both light-tailed and a stationary time for the chain. We note that essentially the same results were obtained independently by Peres and Sousi [arXiv:1108.0133].","authors_text":"Roberto Imbuzeiro Oliveira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-08T13:50:42Z","title":"Mixing and hitting times for finite Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1708","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":"sha256:74c3f5c19a3e4602a323da3ddfc59c0088cc83e761fc0fe4a5c7042538c9c803","target":"record","created_at":"2026-05-18T03:47:01Z","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":"6c45889d9e4212103c3cac83d7290f0032f9dd897d6d0092f4fb78b8a1a0945c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-08T13:50:42Z","title_canon_sha256":"320bea8ff9b20aafef1e28bab4d44b35e7aa306d4dfee072f72045f751360c2f"},"schema_version":"1.0","source":{"id":"1108.1708","kind":"arxiv","version":2}},"canonical_sha256":"b97bfc34773165dd39e3fb5a8257230278f3291d5ef11af7e90f613fea5082cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b97bfc34773165dd39e3fb5a8257230278f3291d5ef11af7e90f613fea5082cb","first_computed_at":"2026-05-18T03:47:01.407567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:01.407567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N/+bRyAGGjXj/wxrxzVGMUMFlHzTbbFuZ5NJLQuwVsAlKFIF3VQHhLKrbVDO6UnQLmLPsv5U9jaVr0QgSV/rBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:01.408091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.1708","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74c3f5c19a3e4602a323da3ddfc59c0088cc83e761fc0fe4a5c7042538c9c803","sha256:da591c7b236fc923c5c2a7d24f6f4b81156a425d20ff16bb7af19f7601b797f2"],"state_sha256":"2ccbcc2428ea5c1c18f4d7f83e1312a71b851935ee4a65dbce875c8e7afabb63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u/wTAIQuEuXXINaHJdhGxYJTT3yG8CHry2t6mJbo+cxuiLbIiDDiLhw5SEA6jsSv2ly1sLx2MtSDkaZkWsRHAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T10:12:20.796922Z","bundle_sha256":"b97d381e9d52381fdce6b3fe42f66759d85b8e40c56bd131ff5a8d03794e2784"}}