{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Q5HKVJP73HGNRIY5LQ652HERDS","short_pith_number":"pith:Q5HKVJP7","canonical_record":{"source":{"id":"1309.0622","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-03T09:04:53Z","cross_cats_sorted":[],"title_canon_sha256":"7ae37132e715bb636a8a23f47165cfe74483847024bf8ca3b6ea555fe64f3f90","abstract_canon_sha256":"0d1128e564d226ee93ac10ec1d0cd1ec0ffdd9b88a89e56608de41bbee324abf"},"schema_version":"1.0"},"canonical_sha256":"874eaaa5ffd9ccd8a31d5c3ddd1c911c8519dd7466d187a10ab16e98d947530f","source":{"kind":"arxiv","id":"1309.0622","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0622","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0622v2","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0622","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"Q5HKVJP73HGN","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q5HKVJP73HGNRIY5","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q5HKVJP7","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Q5HKVJP73HGNRIY5LQ652HERDS","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0622","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-03T09:04:53Z","cross_cats_sorted":[],"title_canon_sha256":"7ae37132e715bb636a8a23f47165cfe74483847024bf8ca3b6ea555fe64f3f90","abstract_canon_sha256":"0d1128e564d226ee93ac10ec1d0cd1ec0ffdd9b88a89e56608de41bbee324abf"},"schema_version":"1.0"},"canonical_sha256":"874eaaa5ffd9ccd8a31d5c3ddd1c911c8519dd7466d187a10ab16e98d947530f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:12.633939Z","signature_b64":"oc1x8sUaHl6Pl9Jys2ZTmnUPXuaiCFw0aHK9KbS4GfTV0P4qqBhmyqNHsCOnYA4B9+KzeoCxJ/CEu8m/z6VtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"874eaaa5ffd9ccd8a31d5c3ddd1c911c8519dd7466d187a10ab16e98d947530f","last_reissued_at":"2026-05-18T02:56:12.633535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:12.633535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0622","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":"2026-05-18T02:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXhDliWpHRuAalj38XLf5UycuNHy5NYXClIMqjKctaydhZDdsJmKxGERk43gtVSjtu1DldI8vpNgMWsOq2dNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:49:48.205631Z"},"content_sha256":"23aabb86c991090eaf7ef75afe2b631cf760b06a7505e9d4ae99846c72317ff3","schema_version":"1.0","event_id":"sha256:23aabb86c991090eaf7ef75afe2b631cf760b06a7505e9d4ae99846c72317ff3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Q5HKVJP73HGNRIY5LQ652HERDS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantitative convergence rates for sub-geometric Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christophe Andrieu, Gersende Fort, Matti Vihola","submitted_at":"2013-09-03T09:04:53Z","abstract_excerpt":"We provide explicit expressions for the constants involved in the characterisation of ergodicity of sub-geometric Markov chains. The constants are determined in terms of those appearing in the assumed drift and one-step minorisation conditions. The result is fundamental for the study of some algorithms where uniform bounds for these constants are needed for a family of Markov kernels. Our result accommodates also some classes of inhomogeneous chains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0622","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":"2026-05-18T02:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8eNa6YJDiM5+hMuBXFUXf2z37OEd7OwZ9HBD49vZ55CYFBQgWn6FcwJrRr8/PGpsbDP41tddcatBF6GHzbu/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:49:48.206128Z"},"content_sha256":"ac3aa36c7fa27280476b7bd729c2a12d14f53a1776b40cec8e86039f07227dfc","schema_version":"1.0","event_id":"sha256:ac3aa36c7fa27280476b7bd729c2a12d14f53a1776b40cec8e86039f07227dfc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q5HKVJP73HGNRIY5LQ652HERDS/bundle.json","state_url":"https://pith.science/pith/Q5HKVJP73HGNRIY5LQ652HERDS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q5HKVJP73HGNRIY5LQ652HERDS/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":"2026-05-30T14:49:48Z","links":{"resolver":"https://pith.science/pith/Q5HKVJP73HGNRIY5LQ652HERDS","bundle":"https://pith.science/pith/Q5HKVJP73HGNRIY5LQ652HERDS/bundle.json","state":"https://pith.science/pith/Q5HKVJP73HGNRIY5LQ652HERDS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q5HKVJP73HGNRIY5LQ652HERDS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q5HKVJP73HGNRIY5LQ652HERDS","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":"0d1128e564d226ee93ac10ec1d0cd1ec0ffdd9b88a89e56608de41bbee324abf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-03T09:04:53Z","title_canon_sha256":"7ae37132e715bb636a8a23f47165cfe74483847024bf8ca3b6ea555fe64f3f90"},"schema_version":"1.0","source":{"id":"1309.0622","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0622","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0622v2","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0622","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"Q5HKVJP73HGN","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q5HKVJP73HGNRIY5","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q5HKVJP7","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:ac3aa36c7fa27280476b7bd729c2a12d14f53a1776b40cec8e86039f07227dfc","target":"graph","created_at":"2026-05-18T02:56:12Z","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 provide explicit expressions for the constants involved in the characterisation of ergodicity of sub-geometric Markov chains. The constants are determined in terms of those appearing in the assumed drift and one-step minorisation conditions. The result is fundamental for the study of some algorithms where uniform bounds for these constants are needed for a family of Markov kernels. Our result accommodates also some classes of inhomogeneous chains.","authors_text":"Christophe Andrieu, Gersende Fort, Matti Vihola","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-03T09:04:53Z","title":"Quantitative convergence rates for sub-geometric Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0622","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":"sha256:23aabb86c991090eaf7ef75afe2b631cf760b06a7505e9d4ae99846c72317ff3","target":"record","created_at":"2026-05-18T02:56:12Z","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":"0d1128e564d226ee93ac10ec1d0cd1ec0ffdd9b88a89e56608de41bbee324abf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-03T09:04:53Z","title_canon_sha256":"7ae37132e715bb636a8a23f47165cfe74483847024bf8ca3b6ea555fe64f3f90"},"schema_version":"1.0","source":{"id":"1309.0622","kind":"arxiv","version":2}},"canonical_sha256":"874eaaa5ffd9ccd8a31d5c3ddd1c911c8519dd7466d187a10ab16e98d947530f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"874eaaa5ffd9ccd8a31d5c3ddd1c911c8519dd7466d187a10ab16e98d947530f","first_computed_at":"2026-05-18T02:56:12.633535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:12.633535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oc1x8sUaHl6Pl9Jys2ZTmnUPXuaiCFw0aHK9KbS4GfTV0P4qqBhmyqNHsCOnYA4B9+KzeoCxJ/CEu8m/z6VtBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:12.633939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0622","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23aabb86c991090eaf7ef75afe2b631cf760b06a7505e9d4ae99846c72317ff3","sha256:ac3aa36c7fa27280476b7bd729c2a12d14f53a1776b40cec8e86039f07227dfc"],"state_sha256":"65649b29bd446914cc0ebb3028415a6da838f5daec5150f6d8f1236e33ad29f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"00WfS/rUmuhgXFF5L48TjrXBIU6NAcYbiKddc55vA1adg0VsKu8hC9hiCqn1k9zlBYBXNSNsSgltdhSaL9+LBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:49:48.209736Z","bundle_sha256":"08972e2fde839fca6f872c6a2bd3f75e235d6e77a99779f118fd9db87cafe7a8"}}