{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TGANKPHNAEA27CMIQ6AS2JCQXR","short_pith_number":"pith:TGANKPHN","canonical_record":{"source":{"id":"1304.4587","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-16T07:20:27Z","cross_cats_sorted":[],"title_canon_sha256":"01c8dd0aa28f2591200334695a140861ebf780e1a5eac977dbf879c4e281f746","abstract_canon_sha256":"2bf9d1ab21adacd649e7f220104c1fd4feb9d00e75e3fc753c5aed631f595a13"},"schema_version":"1.0"},"canonical_sha256":"9980d53ced0101af898887812d2450bc4b6f715e9d33c4b2ba9fbb32c5776675","source":{"kind":"arxiv","id":"1304.4587","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4587","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4587v1","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4587","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"TGANKPHNAEA2","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TGANKPHNAEA27CMI","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TGANKPHN","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TGANKPHNAEA27CMIQ6AS2JCQXR","target":"record","payload":{"canonical_record":{"source":{"id":"1304.4587","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-16T07:20:27Z","cross_cats_sorted":[],"title_canon_sha256":"01c8dd0aa28f2591200334695a140861ebf780e1a5eac977dbf879c4e281f746","abstract_canon_sha256":"2bf9d1ab21adacd649e7f220104c1fd4feb9d00e75e3fc753c5aed631f595a13"},"schema_version":"1.0"},"canonical_sha256":"9980d53ced0101af898887812d2450bc4b6f715e9d33c4b2ba9fbb32c5776675","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:44.266633Z","signature_b64":"I+pnXlS4gUJQCO6oPOhWes2BwPrx+V+Crr8So7Ht3sdQz35PBEw3lNRLT+gJZUGMJdrfa13e5AB0keoK0NblAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9980d53ced0101af898887812d2450bc4b6f715e9d33c4b2ba9fbb32c5776675","last_reissued_at":"2026-05-18T03:27:44.266045Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:44.266045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.4587","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":"2026-05-18T03:27:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tDR/G2Ti1eL8Fd46YejkHKGSjr4wIQTYeVUZ+RbTffvjxCMQZyiMQPwgpQQ88toiGdF/NyFO8Jn/umsNIp8ADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:43:38.293253Z"},"content_sha256":"fc71182d26a79e749d0655e2d48d994a5fa693b048dad62929b01afe05595e11","schema_version":"1.0","event_id":"sha256:fc71182d26a79e749d0655e2d48d994a5fa693b048dad62929b01afe05595e11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TGANKPHNAEA27CMIQ6AS2JCQXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comparison of cutoffs between lazy walks and Markovian semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guan-Yu Chen, Laurent Saloff-Coste","submitted_at":"2013-04-16T07:20:27Z","abstract_excerpt":"We make a connection between the continuous time and lazy discrete time Markov chains through the comparison of cutoffs and mixing time in total variation distance. For illustration, we consider finite birth and death chains and provide a criterion on cutoffs using eigenvalues of the transition matrix."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4587","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":"2026-05-18T03:27:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JcUm0zR4to1TpfxgSQz7UojaH79t2+3Hz2wIgPh8hN7ONU3LkQAbM6NWrB+R70tdqnMohiPWyTUNcL58mbN6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:43:38.293938Z"},"content_sha256":"634a3f85fed5b6192ed49b988d426afc7267c1bc520b8dca7e14872104df3bd2","schema_version":"1.0","event_id":"sha256:634a3f85fed5b6192ed49b988d426afc7267c1bc520b8dca7e14872104df3bd2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TGANKPHNAEA27CMIQ6AS2JCQXR/bundle.json","state_url":"https://pith.science/pith/TGANKPHNAEA27CMIQ6AS2JCQXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TGANKPHNAEA27CMIQ6AS2JCQXR/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":"2026-06-07T16:43:38Z","links":{"resolver":"https://pith.science/pith/TGANKPHNAEA27CMIQ6AS2JCQXR","bundle":"https://pith.science/pith/TGANKPHNAEA27CMIQ6AS2JCQXR/bundle.json","state":"https://pith.science/pith/TGANKPHNAEA27CMIQ6AS2JCQXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TGANKPHNAEA27CMIQ6AS2JCQXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TGANKPHNAEA27CMIQ6AS2JCQXR","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":"2bf9d1ab21adacd649e7f220104c1fd4feb9d00e75e3fc753c5aed631f595a13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-16T07:20:27Z","title_canon_sha256":"01c8dd0aa28f2591200334695a140861ebf780e1a5eac977dbf879c4e281f746"},"schema_version":"1.0","source":{"id":"1304.4587","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4587","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4587v1","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4587","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"TGANKPHNAEA2","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TGANKPHNAEA27CMI","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TGANKPHN","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:634a3f85fed5b6192ed49b988d426afc7267c1bc520b8dca7e14872104df3bd2","target":"graph","created_at":"2026-05-18T03:27:44Z","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 make a connection between the continuous time and lazy discrete time Markov chains through the comparison of cutoffs and mixing time in total variation distance. For illustration, we consider finite birth and death chains and provide a criterion on cutoffs using eigenvalues of the transition matrix.","authors_text":"Guan-Yu Chen, Laurent Saloff-Coste","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-16T07:20:27Z","title":"Comparison of cutoffs between lazy walks and Markovian semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4587","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:fc71182d26a79e749d0655e2d48d994a5fa693b048dad62929b01afe05595e11","target":"record","created_at":"2026-05-18T03:27:44Z","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":"2bf9d1ab21adacd649e7f220104c1fd4feb9d00e75e3fc753c5aed631f595a13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-16T07:20:27Z","title_canon_sha256":"01c8dd0aa28f2591200334695a140861ebf780e1a5eac977dbf879c4e281f746"},"schema_version":"1.0","source":{"id":"1304.4587","kind":"arxiv","version":1}},"canonical_sha256":"9980d53ced0101af898887812d2450bc4b6f715e9d33c4b2ba9fbb32c5776675","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9980d53ced0101af898887812d2450bc4b6f715e9d33c4b2ba9fbb32c5776675","first_computed_at":"2026-05-18T03:27:44.266045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:44.266045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I+pnXlS4gUJQCO6oPOhWes2BwPrx+V+Crr8So7Ht3sdQz35PBEw3lNRLT+gJZUGMJdrfa13e5AB0keoK0NblAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:44.266633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4587","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc71182d26a79e749d0655e2d48d994a5fa693b048dad62929b01afe05595e11","sha256:634a3f85fed5b6192ed49b988d426afc7267c1bc520b8dca7e14872104df3bd2"],"state_sha256":"3660c74bbc564eb2708779623f3201b2afe9c58ed482fbc8e731c68fa5c05f8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a3F4X6xb7f7zwYdZsffzkF7QTQB/lGvuXEQeIm2ujqjR0CfKm9hnv1s7Nxmq0B5q8OLMXjkcb8vEWKYNUNpQAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:43:38.297532Z","bundle_sha256":"54845a908dd4a418e863cadaab529fd07e47920a532be3a8a7b1959c0fd7f440"}}