{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Q3EILB63EDND4M7PUYFCUYD4OW","short_pith_number":"pith:Q3EILB63","canonical_record":{"source":{"id":"1506.02903","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-09T13:30:13Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"d2cc42f17189bd91cae44fee4e72df77030612a865d7c602d71a79695bba3def","abstract_canon_sha256":"e61155efd9b1dc2799f1bb327f5fbe733ff1af43c848f269de478961ffbb610d"},"schema_version":"1.0"},"canonical_sha256":"86c88587db20da3e33efa60a2a607c75b256da2cbb6656e6d5144e97e2cd49b1","source":{"kind":"arxiv","id":"1506.02903","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02903","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02903v3","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02903","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"Q3EILB63EDND","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q3EILB63EDND4M7P","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q3EILB63","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Q3EILB63EDND4M7PUYFCUYD4OW","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02903","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-09T13:30:13Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"d2cc42f17189bd91cae44fee4e72df77030612a865d7c602d71a79695bba3def","abstract_canon_sha256":"e61155efd9b1dc2799f1bb327f5fbe733ff1af43c848f269de478961ffbb610d"},"schema_version":"1.0"},"canonical_sha256":"86c88587db20da3e33efa60a2a607c75b256da2cbb6656e6d5144e97e2cd49b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:06.748680Z","signature_b64":"2BpD6TptFNMCTW85RgTxKLX2Je0EbQMn5xYJfopt0d7GfCbDeNKpC/NUwYaFMeg8i/+7Wjn/TwNgt39Mtc4oCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86c88587db20da3e33efa60a2a607c75b256da2cbb6656e6d5144e97e2cd49b1","last_reissued_at":"2026-05-18T01:28:06.748200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:06.748200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02903","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ux9KRxjSqDR3YKU1wj44w28h9RhHQLAv00sVMjCGssZ2i8V5E8VesU9hDzEj+qFNso4JHE9Vzp5lLoOQwT6/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:39:15.954905Z"},"content_sha256":"024211c31165e05ad3ec4c92326035954965c60304477c7c302042d050409cf1","schema_version":"1.0","event_id":"sha256:024211c31165e05ad3ec4c92326035954965c60304477c7c302042d050409cf1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Q3EILB63EDND4M7PUYFCUYD4OW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixing Time Estimation in Reversible Markov Chains from a Single Sample Path","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Aryeh Kontorovich, Csaba Szepesv\\'ari, Daniel Hsu","submitted_at":"2015-06-09T13:30:13Z","abstract_excerpt":"This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time $t_{\\text{mix}}$ of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from a single finite-length sample path from the Markov chain, and does not require the knowledge of any parameters of the chain. This stands in contrast to previous approaches, which either only provide point estimates, or require a reset mechanism, or additional prior knowledge. The interval is constructed around the relaxation time $t_{\\text{relax}}$, which is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02903","kind":"arxiv","version":3},"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":"2026-05-18T01:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ePMM0b9CjyUB54hl8fMC3tB5itBp9gwxvNCaTVUaUrEW/M9qQp9cqzqZzIqtuzjJM0P/GQ9GK3kQwCcRibNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:39:15.955600Z"},"content_sha256":"c409f14426f49f37dfb0354b91750564455fe6ea2bb05d616ad8789410757081","schema_version":"1.0","event_id":"sha256:c409f14426f49f37dfb0354b91750564455fe6ea2bb05d616ad8789410757081"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3EILB63EDND4M7PUYFCUYD4OW/bundle.json","state_url":"https://pith.science/pith/Q3EILB63EDND4M7PUYFCUYD4OW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3EILB63EDND4M7PUYFCUYD4OW/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":"2026-06-06T16:39:15Z","links":{"resolver":"https://pith.science/pith/Q3EILB63EDND4M7PUYFCUYD4OW","bundle":"https://pith.science/pith/Q3EILB63EDND4M7PUYFCUYD4OW/bundle.json","state":"https://pith.science/pith/Q3EILB63EDND4M7PUYFCUYD4OW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3EILB63EDND4M7PUYFCUYD4OW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Q3EILB63EDND4M7PUYFCUYD4OW","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":"e61155efd9b1dc2799f1bb327f5fbe733ff1af43c848f269de478961ffbb610d","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-09T13:30:13Z","title_canon_sha256":"d2cc42f17189bd91cae44fee4e72df77030612a865d7c602d71a79695bba3def"},"schema_version":"1.0","source":{"id":"1506.02903","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02903","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02903v3","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02903","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"Q3EILB63EDND","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q3EILB63EDND4M7P","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q3EILB63","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:c409f14426f49f37dfb0354b91750564455fe6ea2bb05d616ad8789410757081","target":"graph","created_at":"2026-05-18T01:28:06Z","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":"This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time $t_{\\text{mix}}$ of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from a single finite-length sample path from the Markov chain, and does not require the knowledge of any parameters of the chain. This stands in contrast to previous approaches, which either only provide point estimates, or require a reset mechanism, or additional prior knowledge. The interval is constructed around the relaxation time $t_{\\text{relax}}$, which is","authors_text":"Aryeh Kontorovich, Csaba Szepesv\\'ari, Daniel Hsu","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-09T13:30:13Z","title":"Mixing Time Estimation in Reversible Markov Chains from a Single Sample Path"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02903","kind":"arxiv","version":3},"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":"sha256:024211c31165e05ad3ec4c92326035954965c60304477c7c302042d050409cf1","target":"record","created_at":"2026-05-18T01:28:06Z","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":"e61155efd9b1dc2799f1bb327f5fbe733ff1af43c848f269de478961ffbb610d","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-09T13:30:13Z","title_canon_sha256":"d2cc42f17189bd91cae44fee4e72df77030612a865d7c602d71a79695bba3def"},"schema_version":"1.0","source":{"id":"1506.02903","kind":"arxiv","version":3}},"canonical_sha256":"86c88587db20da3e33efa60a2a607c75b256da2cbb6656e6d5144e97e2cd49b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86c88587db20da3e33efa60a2a607c75b256da2cbb6656e6d5144e97e2cd49b1","first_computed_at":"2026-05-18T01:28:06.748200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:06.748200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2BpD6TptFNMCTW85RgTxKLX2Je0EbQMn5xYJfopt0d7GfCbDeNKpC/NUwYaFMeg8i/+7Wjn/TwNgt39Mtc4oCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:06.748680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02903","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:024211c31165e05ad3ec4c92326035954965c60304477c7c302042d050409cf1","sha256:c409f14426f49f37dfb0354b91750564455fe6ea2bb05d616ad8789410757081"],"state_sha256":"b231d21ef63379d4b08c3c7eb529148007bb3666170332b23058bbfd91042158"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sCtMT+bdKaux+DpWj87UO7OfvjRkGUjt3+G82vzQlxuiohBN2AeVBrGsyyAFjMqUL2B1vC3vhSr5kDvkFTlQBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:39:15.959484Z","bundle_sha256":"2c5b730284c12a5bd568768379ee7b7c920d8150b2867dec0ba138006950f3ab"}}