{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NBTP6D2IIGLNGGPNNYH7LCO376","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":"6447c1fdf43aca1c204c2d6fa1614cdf77bdce4a05a2523a051d8902aee5ee3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-06-27T14:51:34Z","title_canon_sha256":"8c2ed8b009fb897c07d3214e69368d7d21f301768d298bf78eb33f7c601c0fe5"},"schema_version":"1.0","source":{"id":"0906.5083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5083","created_at":"2026-07-04T15:45:16Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5083v1","created_at":"2026-07-04T15:45:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5083","created_at":"2026-07-04T15:45:16Z"},{"alias_kind":"pith_short_12","alias_value":"NBTP6D2IIGLN","created_at":"2026-07-04T15:45:16Z"},{"alias_kind":"pith_short_16","alias_value":"NBTP6D2IIGLNGGPN","created_at":"2026-07-04T15:45:16Z"},{"alias_kind":"pith_short_8","alias_value":"NBTP6D2I","created_at":"2026-07-04T15:45:16Z"}],"graph_snapshots":[{"event_id":"sha256:9851354eef4d070c45883ef6ed451bd7cb3040e21744acf6b9a787f6d4f210e4","target":"graph","created_at":"2026-07-04T15:45:16Z","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/0906.5083/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\{D(s), s \\geq 0 \\}$ be a L\\'evy subordinator, that is, a non-decreasing process with stationary and independent increments and suppose that $D(0) = 0$. We study the first-hitting time of the process $D$, namely, the process $E(t) = \\inf \\{s: D(s) > t \\}$, $t \\geq 0$.\n  The process $E$ is, in general, non-Markovian with non-stationary and non-independent increments. We derive a partial differential equation for the Laplace transform of the $n$-time tail distribution function $P[E(t_1) > s_1,...,E(t_n) > s_n]$, and show that this PDE has a unique solution given natural boundary conditions.","authors_text":"Mark S. Veillette, Murad S. Taqqu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-06-27T14:51:34Z","title":"Using Differential Equations to Obtain Joint Moments of First-Passage Times of Increasing Levy Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5083","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:fe435d354705f64bf6c8c5b94a729037b84c80f36dfceeeb8d290dc62e4acf65","target":"record","created_at":"2026-07-04T15:45:16Z","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":"6447c1fdf43aca1c204c2d6fa1614cdf77bdce4a05a2523a051d8902aee5ee3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-06-27T14:51:34Z","title_canon_sha256":"8c2ed8b009fb897c07d3214e69368d7d21f301768d298bf78eb33f7c601c0fe5"},"schema_version":"1.0","source":{"id":"0906.5083","kind":"arxiv","version":1}},"canonical_sha256":"6866ff0f484196d319ed6e0ff589dbffb5312c808e36bbbeed7cdd35841c3fa4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6866ff0f484196d319ed6e0ff589dbffb5312c808e36bbbeed7cdd35841c3fa4","first_computed_at":"2026-07-04T15:45:16.223642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:45:16.223642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+JFKOnpR/ee/kdZkkWuKtdCTpkHo6KGDZ/CBfME9wxQQgIedf+b8WISg3PyQCRYuM7Fa/gK9GcNxC3LCHNFuAg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:45:16.223982Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.5083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe435d354705f64bf6c8c5b94a729037b84c80f36dfceeeb8d290dc62e4acf65","sha256:9851354eef4d070c45883ef6ed451bd7cb3040e21744acf6b9a787f6d4f210e4"],"state_sha256":"5c0dc1f7c13985e77e351799d4ac528e50926f8d8e4217f1874581ed3503ef43"}