{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7EMY5CHQG2OZS5GRMEV4US6MJK","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":"439a2b04a2e8026ff73414f13a81bd09483ccfdd5d85c963748f08cd52b4920e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-25T19:56:18Z","title_canon_sha256":"f39c476cd0129b5c1341627b1e555e7f06d293e1b9dc7d94fd6d51d039929919"},"schema_version":"1.0","source":{"id":"1205.5793","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5793","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5793v2","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5793","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"7EMY5CHQG2OZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7EMY5CHQG2OZS5GR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7EMY5CHQ","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:fbc8c888ed66eff98fd06875acb5aa437b2d1bec4cb5538f86d66847ed667fce","target":"graph","created_at":"2026-05-18T02:40:54Z","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":"Let ${Z_n}_{n\\ge 0}$ be a random walk with a negative drift and i.i.d. increments with heavy-tailed distribution and let $M=\\sup_{n\\ge 0}Z_n$ be its supremum. Asmussen & Kl{\\\"u}ppelberg (1996) considered the behavior of the random walk given that $M>x$, for $x$ large, and obtained a limit theorem, as $x\\to\\infty$, for the distribution of the quadruple that includes the time $\\rtreg=\\rtreg(x)$ to exceed level $x$, position $Z_{\\rtreg}$ at this time, position $Z_{\\rtreg-1}$ at the prior time, and the trajectory up to it (similar results were obtained for the Cram\\'er-Lundberg insurance risk proc","authors_text":"Sergey Foss, S{\\o}ren Asmussen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-25T19:56:18Z","title":"On exceedance times for some processes with dependent increments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5793","kind":"arxiv","version":2},"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:fdc3afba8140b67ac77a40aab5ad674c88cbb8c2927bef0b524fd92919e68987","target":"record","created_at":"2026-05-18T02:40:54Z","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":"439a2b04a2e8026ff73414f13a81bd09483ccfdd5d85c963748f08cd52b4920e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-25T19:56:18Z","title_canon_sha256":"f39c476cd0129b5c1341627b1e555e7f06d293e1b9dc7d94fd6d51d039929919"},"schema_version":"1.0","source":{"id":"1205.5793","kind":"arxiv","version":2}},"canonical_sha256":"f9198e88f0369d9974d1612bca4bcc4a9bccde6a34545881c0d785a8945936bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9198e88f0369d9974d1612bca4bcc4a9bccde6a34545881c0d785a8945936bf","first_computed_at":"2026-05-18T02:40:54.400174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:54.400174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3uqb3rr7aHPbDlh7nsZaZG++NO+MDZspNRHCCsfN7sCP7VukBAMo9cEqYSYwxWpQXOOfosr8QX/XlSHMlxrsBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:54.400579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5793","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdc3afba8140b67ac77a40aab5ad674c88cbb8c2927bef0b524fd92919e68987","sha256:fbc8c888ed66eff98fd06875acb5aa437b2d1bec4cb5538f86d66847ed667fce"],"state_sha256":"a1bd0b35ef0b12d24a12e9aa35473a13474cdced14515a345241fc1c6471885e"}