{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NDSF3R2LEEOTJICHVZV47WWIIY","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":"42bf3634340224d1929d7ff61fc9ddfe1b9694c0b72909a46b8eab5c424d4c62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-29T12:26:40Z","title_canon_sha256":"009c248df79e05d7d27bd58a8f438dbbb951ef52461eb7e08791b7ceeb2095ad"},"schema_version":"1.0","source":{"id":"1106.5921","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5921","created_at":"2026-05-18T04:05:59Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5921v1","created_at":"2026-05-18T04:05:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5921","created_at":"2026-05-18T04:05:59Z"},{"alias_kind":"pith_short_12","alias_value":"NDSF3R2LEEOT","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NDSF3R2LEEOTJICH","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NDSF3R2L","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:097b0467035988db52579c3d46689547fc06eda554080aecbda7f649a6389bf6","target":"graph","created_at":"2026-05-18T04:05:59Z","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":"We show that if a L\\'evy process creeps then, as a function of $u$, the renewal function $V(t,u)$ of the bivariate ascending ladder process $(L^{-1},H)$ is absolutely continuous on $[0,\\infty)$ and left differentiable on $(0,\\infty)$, and the left derivative at $u$ is proportional to the (improper) distribution function of the time at which the process creeps over level $u$, where the constant of proportionality is $\\rmd_H^{-1}$, the reciprocal of the (positive) drift of $H$. This yields the (missing) term due to creeping in the recent quintuple law of Doney and Kyprianou (2006). As an applica","authors_text":"Philip S. Griffin, Ross A. Maller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-29T12:26:40Z","title":"The time at which a L\\'evy process creeps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5921","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":"sha256:0b06f4bfeec714067c84c8f66c3ccb39a6244a84626f6728f67887fc9e1f898d","target":"record","created_at":"2026-05-18T04:05:59Z","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":"42bf3634340224d1929d7ff61fc9ddfe1b9694c0b72909a46b8eab5c424d4c62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-29T12:26:40Z","title_canon_sha256":"009c248df79e05d7d27bd58a8f438dbbb951ef52461eb7e08791b7ceeb2095ad"},"schema_version":"1.0","source":{"id":"1106.5921","kind":"arxiv","version":1}},"canonical_sha256":"68e45dc74b211d34a047ae6bcfdac8463f5fa7167a732f7785a8dbf7f895e4f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68e45dc74b211d34a047ae6bcfdac8463f5fa7167a732f7785a8dbf7f895e4f6","first_computed_at":"2026-05-18T04:05:59.136465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:59.136465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cdlywbkt/9p40KiT/8aqIWqMMQNZXHgYCy6baMYBGv95FPS811mb+7O6J4dieCuqB2S+9Tj9qlW3gKQywHMrCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:59.137092Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5921","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b06f4bfeec714067c84c8f66c3ccb39a6244a84626f6728f67887fc9e1f898d","sha256:097b0467035988db52579c3d46689547fc06eda554080aecbda7f649a6389bf6"],"state_sha256":"0501862935509a201505e0f5669eaa8d230beb56d025cdd2e8ee09f344123683"}