{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DEG5QAPPKC5H52SXPC7KUMQFY5","short_pith_number":"pith:DEG5QAPP","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"},"canonical_sha256":"190dd801ef50ba7eea5778beaa3205c75c31d4e5b04188c46f52ac2cb75583c5","source":{"kind":"arxiv","id":"1909.13311","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.13311","created_at":"2026-07-05T00:08:09Z"},{"alias_kind":"arxiv_version","alias_value":"1909.13311v1","created_at":"2026-07-05T00:08:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.13311","created_at":"2026-07-05T00:08:09Z"},{"alias_kind":"pith_short_12","alias_value":"DEG5QAPPKC5H","created_at":"2026-07-05T00:08:09Z"},{"alias_kind":"pith_short_16","alias_value":"DEG5QAPPKC5H52SX","created_at":"2026-07-05T00:08:09Z"},{"alias_kind":"pith_short_8","alias_value":"DEG5QAPP","created_at":"2026-07-05T00:08:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DEG5QAPPKC5H52SXPC7KUMQFY5","target":"record","payload":{"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"},"canonical_sha256":"190dd801ef50ba7eea5778beaa3205c75c31d4e5b04188c46f52ac2cb75583c5","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"},"source_kind":"arxiv","source_id":"1909.13311","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":"2026-07-05T00:08:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tlP+motArFcDmL24Fd2DeXWBlsHTx56v/lrZ+VIQRLGoORoB/BcNcRnJCUzmMkzDJt1W/Cd+iffPozuOow+fBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T23:30:13.307853Z"},"content_sha256":"f2adcfca3591e5352eb77db77507dff4716e5f5f5f6ebedb96eec2dab3ef87ad","schema_version":"1.0","event_id":"sha256:f2adcfca3591e5352eb77db77507dff4716e5f5f5f6ebedb96eec2dab3ef87ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DEG5QAPPKC5H52SXPC7KUMQFY5","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:08:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9zzEml6ex1qJ7MhGyKaq/bSM4c2fggYA8oo+bBZpa35KJqjoZQ9k4SWQJGCtY/rX1fFi1rlmevumxfaHxMC7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T23:30:13.308216Z"},"content_sha256":"c2463b7654ad469fb358c5f7be2b2b0d71eae602f4e7482d38852261fb1078e6","schema_version":"1.0","event_id":"sha256:c2463b7654ad469fb358c5f7be2b2b0d71eae602f4e7482d38852261fb1078e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5/bundle.json","state_url":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DEG5QAPPKC5H52SXPC7KUMQFY5/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":"2026-07-06T23:30:13Z","links":{"resolver":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5","bundle":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5/bundle.json","state":"https://pith.science/pith/DEG5QAPPKC5H52SXPC7KUMQFY5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DEG5QAPPKC5H52SXPC7KUMQFY5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DEG5QAPPKC5H52SXPC7KUMQFY5","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":"23e12fb9f475bc489c3e8146cf5580597d452a252bc548a8705d33a604a6bba0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-09-29T16:34:51Z","title_canon_sha256":"f80504c3c63b1954e1f0e0c74f51dbce1e49a6a9e30080bb570d03d62ba5ee43"},"schema_version":"1.0","source":{"id":"1909.13311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.13311","created_at":"2026-07-05T00:08:09Z"},{"alias_kind":"arxiv_version","alias_value":"1909.13311v1","created_at":"2026-07-05T00:08:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.13311","created_at":"2026-07-05T00:08:09Z"},{"alias_kind":"pith_short_12","alias_value":"DEG5QAPPKC5H","created_at":"2026-07-05T00:08:09Z"},{"alias_kind":"pith_short_16","alias_value":"DEG5QAPPKC5H52SX","created_at":"2026-07-05T00:08:09Z"},{"alias_kind":"pith_short_8","alias_value":"DEG5QAPP","created_at":"2026-07-05T00:08:09Z"}],"graph_snapshots":[{"event_id":"sha256:c2463b7654ad469fb358c5f7be2b2b0d71eae602f4e7482d38852261fb1078e6","target":"graph","created_at":"2026-07-05T00:08:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.13311/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Chaoran Hu, Jun Yan, Vladimir Pozdnyakov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-09-29T16:34:51Z","title":"On Occupation Time for On-Off Processes with Multiple Off-States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.13311","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:f2adcfca3591e5352eb77db77507dff4716e5f5f5f6ebedb96eec2dab3ef87ad","target":"record","created_at":"2026-07-05T00:08:09Z","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":"23e12fb9f475bc489c3e8146cf5580597d452a252bc548a8705d33a604a6bba0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-09-29T16:34:51Z","title_canon_sha256":"f80504c3c63b1954e1f0e0c74f51dbce1e49a6a9e30080bb570d03d62ba5ee43"},"schema_version":"1.0","source":{"id":"1909.13311","kind":"arxiv","version":1}},"canonical_sha256":"190dd801ef50ba7eea5778beaa3205c75c31d4e5b04188c46f52ac2cb75583c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"190dd801ef50ba7eea5778beaa3205c75c31d4e5b04188c46f52ac2cb75583c5","first_computed_at":"2026-07-05T00:08:09.195530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:08:09.195530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"79f9ZdfobKr7GYo0kzWY+hpmNFm1ctEUWF+zlrXDwpLYb2Zr4/xBVHxY5Mi43ZeKsqLlorfITAFhlJIuCjnBDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:08:09.195943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.13311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2adcfca3591e5352eb77db77507dff4716e5f5f5f6ebedb96eec2dab3ef87ad","sha256:c2463b7654ad469fb358c5f7be2b2b0d71eae602f4e7482d38852261fb1078e6"],"state_sha256":"e60119e5647ea96130c4d2a6c7b61ec8220cf22d4f27ad87cb46c9c4c82686c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GrkIcSZw06YpU/VnWzE/Syyqz05FVFF4oWDAAP7zK1bZZuGoJyJJTvJHe5WM2gAwUf197UMkg1JCg1aIHA3iAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T23:30:13.310152Z","bundle_sha256":"de24b9bf74852997a84abec1056013c0446bb269c5638fed8db1cc56225fe277"}}