{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HX3XDGE2RZZ2QIBSHNMRSWRHAE","short_pith_number":"pith:HX3XDGE2","canonical_record":{"source":{"id":"1603.05639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-17T19:47:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8157c83fe9db528d32f99ed6a061da23190ec55465752bf2c4158356f6a82785","abstract_canon_sha256":"e902460f4a48ef76d286bc428ffd094e302fae6eb10b44e2a93851df66b53605"},"schema_version":"1.0"},"canonical_sha256":"3df771989a8e73a820323b59195a270113a6d80922cf1be4dd452effbde56ea8","source":{"kind":"arxiv","id":"1603.05639","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05639","created_at":"2026-05-18T01:18:55Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05639v1","created_at":"2026-05-18T01:18:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05639","created_at":"2026-05-18T01:18:55Z"},{"alias_kind":"pith_short_12","alias_value":"HX3XDGE2RZZ2","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HX3XDGE2RZZ2QIBS","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HX3XDGE2","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HX3XDGE2RZZ2QIBSHNMRSWRHAE","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-17T19:47:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8157c83fe9db528d32f99ed6a061da23190ec55465752bf2c4158356f6a82785","abstract_canon_sha256":"e902460f4a48ef76d286bc428ffd094e302fae6eb10b44e2a93851df66b53605"},"schema_version":"1.0"},"canonical_sha256":"3df771989a8e73a820323b59195a270113a6d80922cf1be4dd452effbde56ea8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:55.954912Z","signature_b64":"IW1wSP+TeT4Y0hLVPXxD807QgguLzzUKVu3AiCHzw9cynxEFApYHtcRnjtWO6Rd6Gs9IRujxKyY0HfqsWxzSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3df771989a8e73a820323b59195a270113a6d80922cf1be4dd452effbde56ea8","last_reissued_at":"2026-05-18T01:18:55.954384Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:55.954384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05639","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iBLB4q6IqgzbxGLf7Sr11Muu1AOs3tRWj+Hq9CsO0lySfymufIKlHgBPmmdO76hpUnyOgSFKs2inQjUrvvBpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:18:18.198477Z"},"content_sha256":"19059e6d1112dfa5dbad63a74f5e2b02a598ce911236ef06236d2a359011de47","schema_version":"1.0","event_id":"sha256:19059e6d1112dfa5dbad63a74f5e2b02a598ce911236ef06236d2a359011de47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HX3XDGE2RZZ2QIBSHNMRSWRHAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sensitivity of mixing times in Eulerian digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Lucas Boczkowski, Perla Sousi, Yuval Peres","submitted_at":"2016-03-17T19:47:05Z","abstract_excerpt":"Let $X$ be a lazy random walk on a graph $G$. If $G$ is undirected, then the mixing time is upper bounded by the maximum hitting time of the graph. This fails for directed chains, as the biased random walk on the cycle $\\mathbb{Z}_n$ shows. However, we establish that for Eulerian digraphs, the mixing time is $O(mn)$, where $m$ is the number of edges and $n$ is the number of vertices. In the reversible case, the mixing time is robust to the change of the laziness parameter. Surprisingly, in the directed setting the mixing time can be sensitive to such changes. We also study exploration and cove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05639","kind":"arxiv","version":1},"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":"2026-05-18T01:18:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"312JL5eZ77+nTekQVFvUNxm8MNKNHj12S/gPla+SzCPzc42J7XF0jQV3uMtGOeqnr/nzrixQhAJAgQoWhazYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:18:18.198822Z"},"content_sha256":"69fe74ade278f7481260ded43a32f1187364197e338536261009b7afa18afb29","schema_version":"1.0","event_id":"sha256:69fe74ade278f7481260ded43a32f1187364197e338536261009b7afa18afb29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HX3XDGE2RZZ2QIBSHNMRSWRHAE/bundle.json","state_url":"https://pith.science/pith/HX3XDGE2RZZ2QIBSHNMRSWRHAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HX3XDGE2RZZ2QIBSHNMRSWRHAE/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":"2026-05-28T16:18:18Z","links":{"resolver":"https://pith.science/pith/HX3XDGE2RZZ2QIBSHNMRSWRHAE","bundle":"https://pith.science/pith/HX3XDGE2RZZ2QIBSHNMRSWRHAE/bundle.json","state":"https://pith.science/pith/HX3XDGE2RZZ2QIBSHNMRSWRHAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HX3XDGE2RZZ2QIBSHNMRSWRHAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HX3XDGE2RZZ2QIBSHNMRSWRHAE","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":"e902460f4a48ef76d286bc428ffd094e302fae6eb10b44e2a93851df66b53605","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-17T19:47:05Z","title_canon_sha256":"8157c83fe9db528d32f99ed6a061da23190ec55465752bf2c4158356f6a82785"},"schema_version":"1.0","source":{"id":"1603.05639","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05639","created_at":"2026-05-18T01:18:55Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05639v1","created_at":"2026-05-18T01:18:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05639","created_at":"2026-05-18T01:18:55Z"},{"alias_kind":"pith_short_12","alias_value":"HX3XDGE2RZZ2","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HX3XDGE2RZZ2QIBS","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HX3XDGE2","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:69fe74ade278f7481260ded43a32f1187364197e338536261009b7afa18afb29","target":"graph","created_at":"2026-05-18T01:18:55Z","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 $X$ be a lazy random walk on a graph $G$. If $G$ is undirected, then the mixing time is upper bounded by the maximum hitting time of the graph. This fails for directed chains, as the biased random walk on the cycle $\\mathbb{Z}_n$ shows. However, we establish that for Eulerian digraphs, the mixing time is $O(mn)$, where $m$ is the number of edges and $n$ is the number of vertices. In the reversible case, the mixing time is robust to the change of the laziness parameter. Surprisingly, in the directed setting the mixing time can be sensitive to such changes. We also study exploration and cove","authors_text":"Lucas Boczkowski, Perla Sousi, Yuval Peres","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-17T19:47:05Z","title":"Sensitivity of mixing times in Eulerian digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05639","kind":"arxiv","version":1},"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":"sha256:19059e6d1112dfa5dbad63a74f5e2b02a598ce911236ef06236d2a359011de47","target":"record","created_at":"2026-05-18T01:18:55Z","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":"e902460f4a48ef76d286bc428ffd094e302fae6eb10b44e2a93851df66b53605","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-17T19:47:05Z","title_canon_sha256":"8157c83fe9db528d32f99ed6a061da23190ec55465752bf2c4158356f6a82785"},"schema_version":"1.0","source":{"id":"1603.05639","kind":"arxiv","version":1}},"canonical_sha256":"3df771989a8e73a820323b59195a270113a6d80922cf1be4dd452effbde56ea8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3df771989a8e73a820323b59195a270113a6d80922cf1be4dd452effbde56ea8","first_computed_at":"2026-05-18T01:18:55.954384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:55.954384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IW1wSP+TeT4Y0hLVPXxD807QgguLzzUKVu3AiCHzw9cynxEFApYHtcRnjtWO6Rd6Gs9IRujxKyY0HfqsWxzSBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:55.954912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05639","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19059e6d1112dfa5dbad63a74f5e2b02a598ce911236ef06236d2a359011de47","sha256:69fe74ade278f7481260ded43a32f1187364197e338536261009b7afa18afb29"],"state_sha256":"2231c590764085890e1fceb04e2f44d4c7d856befb8abeae8ceb6218034c98bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ajS0Er6XqYh5i9AcBFa8n5N0SwkBGaG2D3if4zle9Tn21AuYEtqWeCnnfYn8qYszz6zEjBOSblJwAO2SgoFUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:18:18.201746Z","bundle_sha256":"523cbf49b4a3a4fcfde0bcb6b207337a010a184852de8e62aa9043f7b851ae92"}}