{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DEG5QAPPKC5H52SXPC7KUMQFY5","short_pith_number":"pith:DEG5QAPP","schema_version":"1.0","canonical_sha256":"190dd801ef50ba7eea5778beaa3205c75c31d4e5b04188c46f52ac2cb75583c5","source":{"kind":"arxiv","id":"1909.13311","version":1},"attestation_state":"computed","paper":{"title":"On Occupation Time for On-Off Processes with Multiple Off-States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chaoran Hu, Jun Yan, Vladimir Pozdnyakov","submitted_at":"2019-09-29T16:34:51Z","abstract_excerpt":"The need to model a Markov renewal on-off process with multiple off-states arise in many applications such as economics, physics, and engineering. Characterization of the occupation time of one specific off-state marginally or two off-states jointly is crucial to understanding such processes. We derive the exact marginal and joint distributions of the off-state occupation times. The theoretical results are confirmed numerically in a simulation study. A special case when all holding times have Levy distribution is considered for the possibility of simplification of the formulas."},"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":"1909.13311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-09-29T16:34:51Z","cross_cats_sorted":[],"title_canon_sha256":"f80504c3c63b1954e1f0e0c74f51dbce1e49a6a9e30080bb570d03d62ba5ee43","abstract_canon_sha256":"23e12fb9f475bc489c3e8146cf5580597d452a252bc548a8705d33a604a6bba0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:08:09.195943Z","signature_b64":"79f9ZdfobKr7GYo0kzWY+hpmNFm1ctEUWF+zlrXDwpLYb2Zr4/xBVHxY5Mi43ZeKsqLlorfITAFhlJIuCjnBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"190dd801ef50ba7eea5778beaa3205c75c31d4e5b04188c46f52ac2cb75583c5","last_reissued_at":"2026-07-05T00:08:09.195530Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:08:09.195530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Occupation Time for On-Off Processes with Multiple Off-States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chaoran Hu, Jun Yan, Vladimir Pozdnyakov","submitted_at":"2019-09-29T16:34:51Z","abstract_excerpt":"The need to model a Markov renewal on-off process with multiple off-states arise in many applications such as economics, physics, and engineering. Characterization of the occupation time of one specific off-state marginally or two off-states jointly is crucial to understanding such processes. We derive the exact marginal and joint distributions of the off-state occupation times. The theoretical results are confirmed numerically in a simulation study. A special case when all holding times have Levy distribution is considered for the possibility of simplification of the formulas."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.13311","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.13311/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1909.13311","created_at":"2026-07-05T00:08:09.195589+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.13311v1","created_at":"2026-07-05T00:08:09.195589+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.13311","created_at":"2026-07-05T00:08:09.195589+00:00"},{"alias_kind":"pith_short_12","alias_value":"DEG5QAPPKC5H","created_at":"2026-07-05T00:08:09.195589+00:00"},{"alias_kind":"pith_short_16","alias_value":"DEG5QAPPKC5H52SX","created_at":"2026-07-05T00:08:09.195589+00:00"},{"alias_kind":"pith_short_8","alias_value":"DEG5QAPP","created_at":"2026-07-05T00:08:09.195589+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/DEG5QAPPKC5H52SXPC7KUMQFY5","json":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5.json","graph_json":"https://pith.science/api/pith-number/DEG5QAPPKC5H52SXPC7KUMQFY5/graph.json","events_json":"https://pith.science/api/pith-number/DEG5QAPPKC5H52SXPC7KUMQFY5/events.json","paper":"https://pith.science/paper/DEG5QAPP"},"agent_actions":{"view_html":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5","download_json":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5.json","view_paper":"https://pith.science/paper/DEG5QAPP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.13311&json=true","fetch_graph":"https://pith.science/api/pith-number/DEG5QAPPKC5H52SXPC7KUMQFY5/graph.json","fetch_events":"https://pith.science/api/pith-number/DEG5QAPPKC5H52SXPC7KUMQFY5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5/action/storage_attestation","attest_author":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5/action/author_attestation","sign_citation":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5/action/citation_signature","submit_replication":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5/action/replication_record"}},"created_at":"2026-07-05T00:08:09.195589+00:00","updated_at":"2026-07-05T00:08:09.195589+00:00"}