{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q4MOTPWOTYUXKRV52LE7EZV4NQ","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":"59d89e2b2715c78136395f8f3dfccaa905d9745c7dfb01156f717ded3603ee0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-08T13:28:37Z","title_canon_sha256":"c9c4450cd23a72122c9b877cdc49a3f291e425a1525febe83ce928350ede5540"},"schema_version":"1.0","source":{"id":"1401.1692","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1692","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1692v3","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1692","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"Q4MOTPWOTYUX","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q4MOTPWOTYUXKRV5","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q4MOTPWO","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:0f8f5ad0ec83fa9cf73518ab1b73f201e1139052d2d3a7cd3922579e083964b2","target":"graph","created_at":"2026-05-18T01:38:54Z","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 develop Markov chain mixing time estimates for a class of Markov chains with restricted transitions. We assume transitions may occur along a cycle of $n$ nodes and on $n^\\gamma$ additional edges, where $\\gamma < 1$. We find that the mixing times of reversible Markov chains properly interpolate between the mixing times of the cycle with no added edges and of the cycle with $cn$ added edges (which is in turn a Small World Network model). In the case of non-reversible Markov-chains, a considerable gap remains between lower and upper bounds, but simulations give hope to experience a significant","authors_text":"Bal\\'azs Gerencs\\'er","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-08T13:28:37Z","title":"Mixing times of Markov chains on a cycle with additional long range connections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1692","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:eaaf8586d93fecb8f38f81a36a1338b4a975c8c4bb31240be4511fb248164ff4","target":"record","created_at":"2026-05-18T01:38:54Z","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":"59d89e2b2715c78136395f8f3dfccaa905d9745c7dfb01156f717ded3603ee0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-08T13:28:37Z","title_canon_sha256":"c9c4450cd23a72122c9b877cdc49a3f291e425a1525febe83ce928350ede5540"},"schema_version":"1.0","source":{"id":"1401.1692","kind":"arxiv","version":3}},"canonical_sha256":"8718e9bece9e297546bdd2c9f266bc6c16ee88226f3ed5691c59c616e9957a9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8718e9bece9e297546bdd2c9f266bc6c16ee88226f3ed5691c59c616e9957a9a","first_computed_at":"2026-05-18T01:38:54.410822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:54.410822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3q1jhVVzXY1xrr2+wxwcFI0Xhw45hPQhf6vwKKmsey9prtP5P214jaII1MB06rDLZBjNrwG+l9aPa/FEI3ItDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:54.411485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1692","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eaaf8586d93fecb8f38f81a36a1338b4a975c8c4bb31240be4511fb248164ff4","sha256:0f8f5ad0ec83fa9cf73518ab1b73f201e1139052d2d3a7cd3922579e083964b2"],"state_sha256":"b5dc3bd42904035cd727218ca8bb97ab1f74b6cb92b78bf3b6ea9b2245c81a8c"}