{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RL2G3YZYBZTO6RQGPVL7IR4MMA","short_pith_number":"pith:RL2G3YZY","canonical_record":{"source":{"id":"1102.4055","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-20T09:33:00Z","cross_cats_sorted":["math.ST","q-fin.RM","stat.TH"],"title_canon_sha256":"727b996baa3d4a5154524c1d4a1bdd500130977a02773d472e530cf6345dee18","abstract_canon_sha256":"cdc41077c2118c4ed87970277ce94ce1e1e37cd30896d9a87915e5d8af7cc5d8"},"schema_version":"1.0"},"canonical_sha256":"8af46de3380e66ef46067d57f4478c6005dc342fe1e3b2ef465c502b6e8d1ca1","source":{"kind":"arxiv","id":"1102.4055","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4055","created_at":"2026-05-18T03:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4055v2","created_at":"2026-05-18T03:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4055","created_at":"2026-05-18T03:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"RL2G3YZYBZTO","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RL2G3YZYBZTO6RQG","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RL2G3YZY","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RL2G3YZYBZTO6RQGPVL7IR4MMA","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4055","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-20T09:33:00Z","cross_cats_sorted":["math.ST","q-fin.RM","stat.TH"],"title_canon_sha256":"727b996baa3d4a5154524c1d4a1bdd500130977a02773d472e530cf6345dee18","abstract_canon_sha256":"cdc41077c2118c4ed87970277ce94ce1e1e37cd30896d9a87915e5d8af7cc5d8"},"schema_version":"1.0"},"canonical_sha256":"8af46de3380e66ef46067d57f4478c6005dc342fe1e3b2ef465c502b6e8d1ca1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:15.162896Z","signature_b64":"0OowDM8wSLC5ewC2+iseWpqs9sWvMdLmN7xHlLUZlFAX4KLTWCI/3wtwBfo6sm/dgQxg9mwKszNyhKRcQTabAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8af46de3380e66ef46067d57f4478c6005dc342fe1e3b2ef465c502b6e8d1ca1","last_reissued_at":"2026-05-18T03:30:15.162000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:15.162000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4055","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eeChgussTxvasB92sb47c5zudL3YL5XMI6sHcg7c1YJNPh466Fiu5W0V6yq360wHD5cbvhRydQns+UmB0LKJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T16:54:26.836393Z"},"content_sha256":"8f64dbb23343990dacf058da79c7fde2e8f7c1f6d850de3ee04b43c7fbef25ee","schema_version":"1.0","event_id":"sha256:8f64dbb23343990dacf058da79c7fde2e8f7c1f6d850de3ee04b43c7fbef25ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RL2G3YZYBZTO6RQGPVL7IR4MMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parisian ruin probability for spectrally negative L\\'{e}vy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","q-fin.RM","stat.TH"],"primary_cat":"math.PR","authors_text":"Irmina Czarna, Ronnie Loeffen, Zbigniew Palmowski","submitted_at":"2011-02-20T09:33:00Z","abstract_excerpt":"In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period r. The formula involves only the scale function of the spectrally negative Levy process and the distribution of the process at time r."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4055","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ajilfMozL9OwW8tTaxk9GCdwS4VVRmHIHe2ZO30U8YIllAznPLkw+DI4J++IOyCd60CwYNoVMdHMMyC6uzmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T16:54:26.837110Z"},"content_sha256":"7fed522ec9c1c14f189b17f896e1ff81158c5964e4317ad7d97af18d8545135a","schema_version":"1.0","event_id":"sha256:7fed522ec9c1c14f189b17f896e1ff81158c5964e4317ad7d97af18d8545135a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RL2G3YZYBZTO6RQGPVL7IR4MMA/bundle.json","state_url":"https://pith.science/pith/RL2G3YZYBZTO6RQGPVL7IR4MMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RL2G3YZYBZTO6RQGPVL7IR4MMA/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":"2026-05-24T16:54:26Z","links":{"resolver":"https://pith.science/pith/RL2G3YZYBZTO6RQGPVL7IR4MMA","bundle":"https://pith.science/pith/RL2G3YZYBZTO6RQGPVL7IR4MMA/bundle.json","state":"https://pith.science/pith/RL2G3YZYBZTO6RQGPVL7IR4MMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RL2G3YZYBZTO6RQGPVL7IR4MMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RL2G3YZYBZTO6RQGPVL7IR4MMA","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":"cdc41077c2118c4ed87970277ce94ce1e1e37cd30896d9a87915e5d8af7cc5d8","cross_cats_sorted":["math.ST","q-fin.RM","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-20T09:33:00Z","title_canon_sha256":"727b996baa3d4a5154524c1d4a1bdd500130977a02773d472e530cf6345dee18"},"schema_version":"1.0","source":{"id":"1102.4055","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4055","created_at":"2026-05-18T03:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4055v2","created_at":"2026-05-18T03:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4055","created_at":"2026-05-18T03:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"RL2G3YZYBZTO","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RL2G3YZYBZTO6RQG","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RL2G3YZY","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:7fed522ec9c1c14f189b17f896e1ff81158c5964e4317ad7d97af18d8545135a","target":"graph","created_at":"2026-05-18T03:30:15Z","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":"In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period r. The formula involves only the scale function of the spectrally negative Levy process and the distribution of the process at time r.","authors_text":"Irmina Czarna, Ronnie Loeffen, Zbigniew Palmowski","cross_cats":["math.ST","q-fin.RM","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-20T09:33:00Z","title":"Parisian ruin probability for spectrally negative L\\'{e}vy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4055","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":"sha256:8f64dbb23343990dacf058da79c7fde2e8f7c1f6d850de3ee04b43c7fbef25ee","target":"record","created_at":"2026-05-18T03:30:15Z","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":"cdc41077c2118c4ed87970277ce94ce1e1e37cd30896d9a87915e5d8af7cc5d8","cross_cats_sorted":["math.ST","q-fin.RM","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-20T09:33:00Z","title_canon_sha256":"727b996baa3d4a5154524c1d4a1bdd500130977a02773d472e530cf6345dee18"},"schema_version":"1.0","source":{"id":"1102.4055","kind":"arxiv","version":2}},"canonical_sha256":"8af46de3380e66ef46067d57f4478c6005dc342fe1e3b2ef465c502b6e8d1ca1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8af46de3380e66ef46067d57f4478c6005dc342fe1e3b2ef465c502b6e8d1ca1","first_computed_at":"2026-05-18T03:30:15.162000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:15.162000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0OowDM8wSLC5ewC2+iseWpqs9sWvMdLmN7xHlLUZlFAX4KLTWCI/3wtwBfo6sm/dgQxg9mwKszNyhKRcQTabAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:15.162896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4055","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f64dbb23343990dacf058da79c7fde2e8f7c1f6d850de3ee04b43c7fbef25ee","sha256:7fed522ec9c1c14f189b17f896e1ff81158c5964e4317ad7d97af18d8545135a"],"state_sha256":"8bbba7029329370658e1c6518b8e9314f1073a5116ac30d8b851aaa1ebbd89a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JS5V3qVVBJSuxlUECF94Wj4k5PA7Ej3VkFTNH43zFV14SGLv3dpPmLliEIbNfNszR8M+EJ/Zs1qFZRQurLbbBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T16:54:26.841410Z","bundle_sha256":"5f84d5825097085bfb51907c6d9bb4cb6f02d4f426ee035f3661b6a0ee5c1d5b"}}