{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Y642FYZKLEZ2GBG4VZHXT35KQK","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":"53ae1a7196e21c3edbb47b918cfcddd1be3d8ebf0a9c959665c7472414529250","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-30T09:46:27Z","title_canon_sha256":"e11617107bb38f5b4f8ea823e616099e77ec7d7984c752b915a9f94e6482ba9f"},"schema_version":"1.0","source":{"id":"1301.7180","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7180","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7180v1","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7180","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"pith_short_12","alias_value":"Y642FYZKLEZ2","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y642FYZKLEZ2GBG4","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y642FYZK","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:e97153845f09d6598ee372c01eb32e34ae55d7b92ffc2a0e1a3d8537bfedab95","target":"graph","created_at":"2026-05-18T03:35:01Z","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":"A well-known theorem for an irreducible skip-free chain with absorbing state $d$, under some conditions, is that the hitting (absorbing) time of state $d$ starting from state 0 is distributed as the sum of $d$ independent geometric (or exponential) random variables. The purpose of this paper is to present a direct and simple proof of the theorem in the cases of both discrete and continuous time skip-free Markov chains. Our proof is to calculate directly the generation functions (or Laplace transforms) of hitting times in terms of the iteration method.","authors_text":"Ke Zhou, Wenming Hong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-30T09:46:27Z","title":"Hitting Time Distribution for Skip-Free Markov Chains: A Simple Proof"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7180","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":"sha256:492ae67623b0382a37ef94e6f8d700b54b4642ee9be72686d7dbe587375e7f24","target":"record","created_at":"2026-05-18T03:35:01Z","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":"53ae1a7196e21c3edbb47b918cfcddd1be3d8ebf0a9c959665c7472414529250","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-30T09:46:27Z","title_canon_sha256":"e11617107bb38f5b4f8ea823e616099e77ec7d7984c752b915a9f94e6482ba9f"},"schema_version":"1.0","source":{"id":"1301.7180","kind":"arxiv","version":1}},"canonical_sha256":"c7b9a2e32a5933a304dcae4f79efaa82b00bb72b3a904bab1ab3b18617700256","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7b9a2e32a5933a304dcae4f79efaa82b00bb72b3a904bab1ab3b18617700256","first_computed_at":"2026-05-18T03:35:01.067371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:01.067371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9zA6Lk8fpbJ2vUgjr0wHlaM+0Zbxs99ufKtNZPD8ihW8z8dys7+ysh2NwPPKv6BhNHQtWXsR1FB6mrGcIqc4Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:01.068116Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.7180","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:492ae67623b0382a37ef94e6f8d700b54b4642ee9be72686d7dbe587375e7f24","sha256:e97153845f09d6598ee372c01eb32e34ae55d7b92ffc2a0e1a3d8537bfedab95"],"state_sha256":"455ec950da401223aaff6484c65199bceed5f294f3a0215d2a46a07538abb751"}