{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GEMM3QVX5H6NOMMN5N4XAPCLX6","short_pith_number":"pith:GEMM3QVX","canonical_record":{"source":{"id":"1409.1745","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-05T11:42:51Z","cross_cats_sorted":[],"title_canon_sha256":"efb2a3b2e2cfbfdfab6573ebd909e3c7be5e45483f5807e4d154df8d1086cfdf","abstract_canon_sha256":"7c4818574506cbfc45a70485a094c1764ee91ff3f88292d6080d448a4dda2312"},"schema_version":"1.0"},"canonical_sha256":"3118cdc2b7e9fcd7318deb79703c4bbfa7248cff53a185a0f8a4c9dfc4f1e31b","source":{"kind":"arxiv","id":"1409.1745","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1745","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1745v1","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1745","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"pith_short_12","alias_value":"GEMM3QVX5H6N","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GEMM3QVX5H6NOMMN","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GEMM3QVX","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GEMM3QVX5H6NOMMN5N4XAPCLX6","target":"record","payload":{"canonical_record":{"source":{"id":"1409.1745","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-05T11:42:51Z","cross_cats_sorted":[],"title_canon_sha256":"efb2a3b2e2cfbfdfab6573ebd909e3c7be5e45483f5807e4d154df8d1086cfdf","abstract_canon_sha256":"7c4818574506cbfc45a70485a094c1764ee91ff3f88292d6080d448a4dda2312"},"schema_version":"1.0"},"canonical_sha256":"3118cdc2b7e9fcd7318deb79703c4bbfa7248cff53a185a0f8a4c9dfc4f1e31b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:25.322762Z","signature_b64":"ATtD6/5DIJpI/HGIsF/oIsiITQzcU9jfka6riNyxsvejeV7z+vg6iEl1zC/phCBxWSgNl0k2R73Uxe1vVb5iDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3118cdc2b7e9fcd7318deb79703c4bbfa7248cff53a185a0f8a4c9dfc4f1e31b","last_reissued_at":"2026-05-18T02:43:25.322142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:25.322142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.1745","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":"2026-05-18T02:43:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lEpLiEJMPo1tdKmKyVa+R9jkNlqfFNEKff4b5wr/DuYJLvp+vHoo1Oes2Q9Dhij11D4LjRntTTxqq4Fat8QgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:53:50.073366Z"},"content_sha256":"e054eafaabe3740e76b1c9c0cae17e245b788b70c466915c49981c3987f88a49","schema_version":"1.0","event_id":"sha256:e054eafaabe3740e76b1c9c0cae17e245b788b70c466915c49981c3987f88a49"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GEMM3QVX5H6NOMMN5N4XAPCLX6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quickest detection of a hidden target and extremal surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Goran Peskir","submitted_at":"2014-09-05T11:42:51Z","abstract_excerpt":"Let $Z=(Z_t)_{t\\ge0}$ be a regular diffusion process started at $0$, let $\\ell$ be an independent random variable with a strictly increasing and continuous distribution function $F$, and let $\\tau_{\\ell}=\\inf\\{t\\ge0\\vert Z_t=\\ell\\}$ be the first entry time of $Z$ at the level $\\ell$. We show that the quickest detection problem \\[\\inf_{\\tau}\\bigl[\\mathsf{P}(\\tau<\\tau_{\\ell})+c\\mathsf{E}(\\tau -\\tau_{\\ell})^+\\bigr]\\] is equivalent to the (three-dimensional) optimal stopping problem \\[\\sup_{\\tau}\\mathsf{E}\\biggl[R_{\\tau}-\\int _0^{\\tau}c(R_t)\\,dt\\biggr],\\] where $R=S-I$ is the range process of $X=2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1745","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":"2026-05-18T02:43:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"17APyrThKahdcxjrnR73VIsLQHnsc7kKcn/8JG71iBXg78ERwWiOM+OhIQWakpKMPG0WcABxod0hatkl1IleCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:53:50.074024Z"},"content_sha256":"6d9c8d6422e8bad8a6427bbf43a2d3d4de313a69cde3a68edea24badf0b68aa2","schema_version":"1.0","event_id":"sha256:6d9c8d6422e8bad8a6427bbf43a2d3d4de313a69cde3a68edea24badf0b68aa2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6/bundle.json","state_url":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6/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":"2026-06-11T15:53:50Z","links":{"resolver":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6","bundle":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6/bundle.json","state":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GEMM3QVX5H6NOMMN5N4XAPCLX6","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":"7c4818574506cbfc45a70485a094c1764ee91ff3f88292d6080d448a4dda2312","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-05T11:42:51Z","title_canon_sha256":"efb2a3b2e2cfbfdfab6573ebd909e3c7be5e45483f5807e4d154df8d1086cfdf"},"schema_version":"1.0","source":{"id":"1409.1745","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1745","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1745v1","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1745","created_at":"2026-05-18T02:43:25Z"},{"alias_kind":"pith_short_12","alias_value":"GEMM3QVX5H6N","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GEMM3QVX5H6NOMMN","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GEMM3QVX","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:6d9c8d6422e8bad8a6427bbf43a2d3d4de313a69cde3a68edea24badf0b68aa2","target":"graph","created_at":"2026-05-18T02:43:25Z","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 $Z=(Z_t)_{t\\ge0}$ be a regular diffusion process started at $0$, let $\\ell$ be an independent random variable with a strictly increasing and continuous distribution function $F$, and let $\\tau_{\\ell}=\\inf\\{t\\ge0\\vert Z_t=\\ell\\}$ be the first entry time of $Z$ at the level $\\ell$. We show that the quickest detection problem \\[\\inf_{\\tau}\\bigl[\\mathsf{P}(\\tau<\\tau_{\\ell})+c\\mathsf{E}(\\tau -\\tau_{\\ell})^+\\bigr]\\] is equivalent to the (three-dimensional) optimal stopping problem \\[\\sup_{\\tau}\\mathsf{E}\\biggl[R_{\\tau}-\\int _0^{\\tau}c(R_t)\\,dt\\biggr],\\] where $R=S-I$ is the range process of $X=2","authors_text":"Goran Peskir","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-05T11:42:51Z","title":"Quickest detection of a hidden target and extremal surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1745","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:e054eafaabe3740e76b1c9c0cae17e245b788b70c466915c49981c3987f88a49","target":"record","created_at":"2026-05-18T02:43:25Z","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":"7c4818574506cbfc45a70485a094c1764ee91ff3f88292d6080d448a4dda2312","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-05T11:42:51Z","title_canon_sha256":"efb2a3b2e2cfbfdfab6573ebd909e3c7be5e45483f5807e4d154df8d1086cfdf"},"schema_version":"1.0","source":{"id":"1409.1745","kind":"arxiv","version":1}},"canonical_sha256":"3118cdc2b7e9fcd7318deb79703c4bbfa7248cff53a185a0f8a4c9dfc4f1e31b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3118cdc2b7e9fcd7318deb79703c4bbfa7248cff53a185a0f8a4c9dfc4f1e31b","first_computed_at":"2026-05-18T02:43:25.322142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:25.322142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ATtD6/5DIJpI/HGIsF/oIsiITQzcU9jfka6riNyxsvejeV7z+vg6iEl1zC/phCBxWSgNl0k2R73Uxe1vVb5iDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:25.322762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1745","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e054eafaabe3740e76b1c9c0cae17e245b788b70c466915c49981c3987f88a49","sha256:6d9c8d6422e8bad8a6427bbf43a2d3d4de313a69cde3a68edea24badf0b68aa2"],"state_sha256":"c051b8d0400c5a34791db64ab28f8452779f0718fed3dd595baf573e96506cba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kaCtXPSO4yVC61mRh9AlBcI/uBFDeIxBN6YzCIzwbsnFsm4GGuh2PRWk6BW22Wclp5niXvf+GD2ijQRZC9XDCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T15:53:50.076731Z","bundle_sha256":"abda4fdd9f5a83c2bee8bb4792b1d20f4578ecd3cc9da815f4d8f9941aa39573"}}