{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VCXXRGCMI2P4C4ZWWDRA2Z6WIC","short_pith_number":"pith:VCXXRGCM","canonical_record":{"source":{"id":"1603.05895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-18T15:34:51Z","cross_cats_sorted":[],"title_canon_sha256":"e2a98b5a6a7af6d27645cd12590efd85c6e592b231f4d821e7e5ff4caa2ae10c","abstract_canon_sha256":"d551a7f7e4a8533fe0a1ca68641bfc8a8f91048c1091bd025016e70e0b699aaa"},"schema_version":"1.0"},"canonical_sha256":"a8af78984c469fc17336b0e20d67d640905fdbbc4fa6263011b25eb76c7ecd2b","source":{"kind":"arxiv","id":"1603.05895","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05895","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05895v2","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05895","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"VCXXRGCMI2P4","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VCXXRGCMI2P4C4ZW","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VCXXRGCM","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VCXXRGCMI2P4C4ZWWDRA2Z6WIC","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-18T15:34:51Z","cross_cats_sorted":[],"title_canon_sha256":"e2a98b5a6a7af6d27645cd12590efd85c6e592b231f4d821e7e5ff4caa2ae10c","abstract_canon_sha256":"d551a7f7e4a8533fe0a1ca68641bfc8a8f91048c1091bd025016e70e0b699aaa"},"schema_version":"1.0"},"canonical_sha256":"a8af78984c469fc17336b0e20d67d640905fdbbc4fa6263011b25eb76c7ecd2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:09.135975Z","signature_b64":"ma9wjrqBLqQfsMX3APxjypHbR8fadWAkhJEuvHbLBY1dzjA/XOpIMbIHAphMXj3c6uyhwda9mRMiQ5wN5vnjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8af78984c469fc17336b0e20d67d640905fdbbc4fa6263011b25eb76c7ecd2b","last_reissued_at":"2026-05-18T01:16:09.135496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:09.135496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05895","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":"2026-05-18T01:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wCsrJBTTQKCWohWPJ8XAd+mIwsS4zYfqL12in9qD+C9OWULDSXSYr0fy4rsp6LXKLeYmPgCBU0eYaQcDJ8x7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:34:36.033782Z"},"content_sha256":"e97e138b7a1772fd99e13e6f4d05df5071c060c61e993b7d9c8933d1fd6eecb1","schema_version":"1.0","event_id":"sha256:e97e138b7a1772fd99e13e6f4d05df5071c060c61e993b7d9c8933d1fd6eecb1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VCXXRGCMI2P4C4ZWWDRA2Z6WIC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics for Quasi-Stationary Distributions of Perturbed Discrete Time Semi-Markov Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mikael Petersson","submitted_at":"2016-03-18T15:34:51Z","abstract_excerpt":"In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are expected to persist for a long time. We obtain asymptotic power series expansions for quasi-stationary distributions and it is shown how the coefficients in these expansions can be computed from a recursive algorithm. As an illustration of this algorithm, we present a numerical example for a discrete time Markov chain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05895","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":"2026-05-18T01:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4fJTFPKtQKmAf3OS4J559mL0Y/WMVtg8NcTqKbyZ/P6QPeoPYQ8rWcb8VUbKSL40EE6aYzLC2obgDNvztk5uDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:34:36.034120Z"},"content_sha256":"b1a4761d62f713defff70afe0dc1d2024a352c8c35a5a261728b2071c661dfc3","schema_version":"1.0","event_id":"sha256:b1a4761d62f713defff70afe0dc1d2024a352c8c35a5a261728b2071c661dfc3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCXXRGCMI2P4C4ZWWDRA2Z6WIC/bundle.json","state_url":"https://pith.science/pith/VCXXRGCMI2P4C4ZWWDRA2Z6WIC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCXXRGCMI2P4C4ZWWDRA2Z6WIC/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":"2026-06-28T10:34:36Z","links":{"resolver":"https://pith.science/pith/VCXXRGCMI2P4C4ZWWDRA2Z6WIC","bundle":"https://pith.science/pith/VCXXRGCMI2P4C4ZWWDRA2Z6WIC/bundle.json","state":"https://pith.science/pith/VCXXRGCMI2P4C4ZWWDRA2Z6WIC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCXXRGCMI2P4C4ZWWDRA2Z6WIC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VCXXRGCMI2P4C4ZWWDRA2Z6WIC","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":"d551a7f7e4a8533fe0a1ca68641bfc8a8f91048c1091bd025016e70e0b699aaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-18T15:34:51Z","title_canon_sha256":"e2a98b5a6a7af6d27645cd12590efd85c6e592b231f4d821e7e5ff4caa2ae10c"},"schema_version":"1.0","source":{"id":"1603.05895","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05895","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05895v2","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05895","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"VCXXRGCMI2P4","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VCXXRGCMI2P4C4ZW","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VCXXRGCM","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:b1a4761d62f713defff70afe0dc1d2024a352c8c35a5a261728b2071c661dfc3","target":"graph","created_at":"2026-05-18T01:16:09Z","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":"In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are expected to persist for a long time. We obtain asymptotic power series expansions for quasi-stationary distributions and it is shown how the coefficients in these expansions can be computed from a recursive algorithm. As an illustration of this algorithm, we present a numerical example for a discrete time Markov chain.","authors_text":"Mikael Petersson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-18T15:34:51Z","title":"Asymptotics for Quasi-Stationary Distributions of Perturbed Discrete Time Semi-Markov Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05895","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:e97e138b7a1772fd99e13e6f4d05df5071c060c61e993b7d9c8933d1fd6eecb1","target":"record","created_at":"2026-05-18T01:16:09Z","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":"d551a7f7e4a8533fe0a1ca68641bfc8a8f91048c1091bd025016e70e0b699aaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-18T15:34:51Z","title_canon_sha256":"e2a98b5a6a7af6d27645cd12590efd85c6e592b231f4d821e7e5ff4caa2ae10c"},"schema_version":"1.0","source":{"id":"1603.05895","kind":"arxiv","version":2}},"canonical_sha256":"a8af78984c469fc17336b0e20d67d640905fdbbc4fa6263011b25eb76c7ecd2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8af78984c469fc17336b0e20d67d640905fdbbc4fa6263011b25eb76c7ecd2b","first_computed_at":"2026-05-18T01:16:09.135496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:09.135496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ma9wjrqBLqQfsMX3APxjypHbR8fadWAkhJEuvHbLBY1dzjA/XOpIMbIHAphMXj3c6uyhwda9mRMiQ5wN5vnjAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:09.135975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05895","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e97e138b7a1772fd99e13e6f4d05df5071c060c61e993b7d9c8933d1fd6eecb1","sha256:b1a4761d62f713defff70afe0dc1d2024a352c8c35a5a261728b2071c661dfc3"],"state_sha256":"18d3fc5ab27e9f7cf0eaef54bbcb1194a1624603977f46cd917f090574baa858"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJjlF/X6RhdUCYOQtQGeXsPHpov1h/VyK9N+FbrtmgQ9XdMW+zlC3+eJ0u8+R7CYc7/LOYUxc8F5VfqTz4fcBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T10:34:36.036074Z","bundle_sha256":"4032768d210ac0fe91ff424e37c14984b5b37f49d93eeace70df4573be04ccd9"}}