{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VYPXZ6C3Z52LK7JAEBTJKKHOXQ","short_pith_number":"pith:VYPXZ6C3","canonical_record":{"source":{"id":"1806.03201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-08T14:50:12Z","cross_cats_sorted":[],"title_canon_sha256":"8c84542222d7b6979d4656d5a1249e061f7e9e55365281da796cdabe4daacaed","abstract_canon_sha256":"ef4f0ef6fd9b4608af24a6f5843e490f4b7b43479f7afdcb311b304882bd2b4a"},"schema_version":"1.0"},"canonical_sha256":"ae1f7cf85bcf74b57d2020669528eebc155030de711531128e5455fa2f1cc7fc","source":{"kind":"arxiv","id":"1806.03201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03201","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03201v1","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03201","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"pith_short_12","alias_value":"VYPXZ6C3Z52L","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VYPXZ6C3Z52LK7JA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VYPXZ6C3","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VYPXZ6C3Z52LK7JAEBTJKKHOXQ","target":"record","payload":{"canonical_record":{"source":{"id":"1806.03201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-08T14:50:12Z","cross_cats_sorted":[],"title_canon_sha256":"8c84542222d7b6979d4656d5a1249e061f7e9e55365281da796cdabe4daacaed","abstract_canon_sha256":"ef4f0ef6fd9b4608af24a6f5843e490f4b7b43479f7afdcb311b304882bd2b4a"},"schema_version":"1.0"},"canonical_sha256":"ae1f7cf85bcf74b57d2020669528eebc155030de711531128e5455fa2f1cc7fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:49.273597Z","signature_b64":"S01515hDUOEef0t1L1Mr0Fyw9/3N9FZ9I1pYW97qC+p0UOi8YOdxh3eOAK2CxgXrhEQUodoOHD7hS3KFr5idCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae1f7cf85bcf74b57d2020669528eebc155030de711531128e5455fa2f1cc7fc","last_reissued_at":"2026-05-18T00:13:49.272976Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:49.272976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.03201","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":"2026-05-18T00:13:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KsDNZA7x6OCGeP3rrKTd8mvr0PrC9Mi4JvanqiYWLuMvDPx8nSSvcDyZW0AOS0neGXsrMP5XL0ZyQQqSM3HGAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:23:20.733843Z"},"content_sha256":"662d896b81392cd479cfe648df372a94c95a21ecbe050a73b45aa08c86c8ecab","schema_version":"1.0","event_id":"sha256:662d896b81392cd479cfe648df372a94c95a21ecbe050a73b45aa08c86c8ecab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VYPXZ6C3Z52LK7JAEBTJKKHOXQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How long does the surplus stay close to its historical high?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bo Li, Xiaowen Zhou, Yun Hua","submitted_at":"2018-06-08T14:50:12Z","abstract_excerpt":"In this paper we find the Laplace transforms of the weighted occupation times for a spectrally negative L\\'evy surplus process to spend below its running maximum up to the first exit times. The results are expressed in terms of generalized scale functions. For step weight functions, the Laplace transforms can be further expressed in terms of scale functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03201","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":""},"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":"2026-05-18T00:13:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XT0aCBn3yJGQ1lDMrwEPqpF/E50yPXbWAzPkIyzJboGLaj693UnzNLDwrTH66ZxcCvL1WuzMCsKWe8OJAXBSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:23:20.734559Z"},"content_sha256":"7696208f81dff4fcd75b9a1e47d9e4437ce773264dc7745b9950730b9b2ee246","schema_version":"1.0","event_id":"sha256:7696208f81dff4fcd75b9a1e47d9e4437ce773264dc7745b9950730b9b2ee246"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYPXZ6C3Z52LK7JAEBTJKKHOXQ/bundle.json","state_url":"https://pith.science/pith/VYPXZ6C3Z52LK7JAEBTJKKHOXQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYPXZ6C3Z52LK7JAEBTJKKHOXQ/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":"2026-05-26T09:23:20Z","links":{"resolver":"https://pith.science/pith/VYPXZ6C3Z52LK7JAEBTJKKHOXQ","bundle":"https://pith.science/pith/VYPXZ6C3Z52LK7JAEBTJKKHOXQ/bundle.json","state":"https://pith.science/pith/VYPXZ6C3Z52LK7JAEBTJKKHOXQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYPXZ6C3Z52LK7JAEBTJKKHOXQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VYPXZ6C3Z52LK7JAEBTJKKHOXQ","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":"ef4f0ef6fd9b4608af24a6f5843e490f4b7b43479f7afdcb311b304882bd2b4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-08T14:50:12Z","title_canon_sha256":"8c84542222d7b6979d4656d5a1249e061f7e9e55365281da796cdabe4daacaed"},"schema_version":"1.0","source":{"id":"1806.03201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03201","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03201v1","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03201","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"pith_short_12","alias_value":"VYPXZ6C3Z52L","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VYPXZ6C3Z52LK7JA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VYPXZ6C3","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:7696208f81dff4fcd75b9a1e47d9e4437ce773264dc7745b9950730b9b2ee246","target":"graph","created_at":"2026-05-18T00:13:49Z","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 paper we find the Laplace transforms of the weighted occupation times for a spectrally negative L\\'evy surplus process to spend below its running maximum up to the first exit times. The results are expressed in terms of generalized scale functions. For step weight functions, the Laplace transforms can be further expressed in terms of scale functions.","authors_text":"Bo Li, Xiaowen Zhou, Yun Hua","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-08T14:50:12Z","title":"How long does the surplus stay close to its historical high?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03201","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":"sha256:662d896b81392cd479cfe648df372a94c95a21ecbe050a73b45aa08c86c8ecab","target":"record","created_at":"2026-05-18T00:13:49Z","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":"ef4f0ef6fd9b4608af24a6f5843e490f4b7b43479f7afdcb311b304882bd2b4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-08T14:50:12Z","title_canon_sha256":"8c84542222d7b6979d4656d5a1249e061f7e9e55365281da796cdabe4daacaed"},"schema_version":"1.0","source":{"id":"1806.03201","kind":"arxiv","version":1}},"canonical_sha256":"ae1f7cf85bcf74b57d2020669528eebc155030de711531128e5455fa2f1cc7fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae1f7cf85bcf74b57d2020669528eebc155030de711531128e5455fa2f1cc7fc","first_computed_at":"2026-05-18T00:13:49.272976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:49.272976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S01515hDUOEef0t1L1Mr0Fyw9/3N9FZ9I1pYW97qC+p0UOi8YOdxh3eOAK2CxgXrhEQUodoOHD7hS3KFr5idCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:49.273597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:662d896b81392cd479cfe648df372a94c95a21ecbe050a73b45aa08c86c8ecab","sha256:7696208f81dff4fcd75b9a1e47d9e4437ce773264dc7745b9950730b9b2ee246"],"state_sha256":"cb1d574c0c70ce1db004748ba54afc8ccf508cb3549df47ade54685e51a01a70"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"awipXu+/AaX1EB1ZB0omEH07FjZSElXLVLkgnAb7nOMcLvz9kpVieuRC8gbG6YmBopEqtIxhPL1Uz5sX1JchCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:23:20.738394Z","bundle_sha256":"4f31ff7efe3cbc4b72022baeef7ab50bd73c0b2a4066d92dc865a1f507ba3ae2"}}