{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:Y642FYZKLEZ2GBG4VZHXT35KQK","short_pith_number":"pith:Y642FYZK","schema_version":"1.0","canonical_sha256":"c7b9a2e32a5933a304dcae4f79efaa82b00bb72b3a904bab1ab3b18617700256","source":{"kind":"arxiv","id":"1301.7180","version":1},"attestation_state":"computed","paper":{"title":"Hitting Time Distribution for Skip-Free Markov Chains: A Simple Proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ke Zhou, Wenming Hong","submitted_at":"2013-01-30T09:46:27Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.7180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-30T09:46:27Z","cross_cats_sorted":[],"title_canon_sha256":"e11617107bb38f5b4f8ea823e616099e77ec7d7984c752b915a9f94e6482ba9f","abstract_canon_sha256":"53ae1a7196e21c3edbb47b918cfcddd1be3d8ebf0a9c959665c7472414529250"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:01.068116Z","signature_b64":"9zA6Lk8fpbJ2vUgjr0wHlaM+0Zbxs99ufKtNZPD8ihW8z8dys7+ysh2NwPPKv6BhNHQtWXsR1FB6mrGcIqc4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7b9a2e32a5933a304dcae4f79efaa82b00bb72b3a904bab1ab3b18617700256","last_reissued_at":"2026-05-18T03:35:01.067371Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:01.067371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hitting Time Distribution for Skip-Free Markov Chains: A Simple Proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ke Zhou, Wenming Hong","submitted_at":"2013-01-30T09:46:27Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7180","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.7180","created_at":"2026-05-18T03:35:01.067506+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.7180v1","created_at":"2026-05-18T03:35:01.067506+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7180","created_at":"2026-05-18T03:35:01.067506+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y642FYZKLEZ2","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y642FYZKLEZ2GBG4","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y642FYZK","created_at":"2026-05-18T12:28:06.772260+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y642FYZKLEZ2GBG4VZHXT35KQK","json":"https://pith.science/pith/Y642FYZKLEZ2GBG4VZHXT35KQK.json","graph_json":"https://pith.science/api/pith-number/Y642FYZKLEZ2GBG4VZHXT35KQK/graph.json","events_json":"https://pith.science/api/pith-number/Y642FYZKLEZ2GBG4VZHXT35KQK/events.json","paper":"https://pith.science/paper/Y642FYZK"},"agent_actions":{"view_html":"https://pith.science/pith/Y642FYZKLEZ2GBG4VZHXT35KQK","download_json":"https://pith.science/pith/Y642FYZKLEZ2GBG4VZHXT35KQK.json","view_paper":"https://pith.science/paper/Y642FYZK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.7180&json=true","fetch_graph":"https://pith.science/api/pith-number/Y642FYZKLEZ2GBG4VZHXT35KQK/graph.json","fetch_events":"https://pith.science/api/pith-number/Y642FYZKLEZ2GBG4VZHXT35KQK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y642FYZKLEZ2GBG4VZHXT35KQK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y642FYZKLEZ2GBG4VZHXT35KQK/action/storage_attestation","attest_author":"https://pith.science/pith/Y642FYZKLEZ2GBG4VZHXT35KQK/action/author_attestation","sign_citation":"https://pith.science/pith/Y642FYZKLEZ2GBG4VZHXT35KQK/action/citation_signature","submit_replication":"https://pith.science/pith/Y642FYZKLEZ2GBG4VZHXT35KQK/action/replication_record"}},"created_at":"2026-05-18T03:35:01.067506+00:00","updated_at":"2026-05-18T03:35:01.067506+00:00"}