{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LQWJR3KQSHX7AWXZUEYOYMYI7I","short_pith_number":"pith:LQWJR3KQ","canonical_record":{"source":{"id":"1808.01852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-06T12:40:07Z","cross_cats_sorted":[],"title_canon_sha256":"2bf11fb3d682d5d5c0aff75f93151c0a83fec693138cc3055c8692b6a9826bd3","abstract_canon_sha256":"0115065419a506d8d7644a8caca02b8719d3718c5e9a33f4a2df85e7820981dc"},"schema_version":"1.0"},"canonical_sha256":"5c2c98ed5091eff05af9a130ec3308fa369f97de7f0f49b72eb63d974f09d88c","source":{"kind":"arxiv","id":"1808.01852","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01852","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01852v2","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01852","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"LQWJR3KQSHX7","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LQWJR3KQSHX7AWXZ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LQWJR3KQ","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LQWJR3KQSHX7AWXZUEYOYMYI7I","target":"record","payload":{"canonical_record":{"source":{"id":"1808.01852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-06T12:40:07Z","cross_cats_sorted":[],"title_canon_sha256":"2bf11fb3d682d5d5c0aff75f93151c0a83fec693138cc3055c8692b6a9826bd3","abstract_canon_sha256":"0115065419a506d8d7644a8caca02b8719d3718c5e9a33f4a2df85e7820981dc"},"schema_version":"1.0"},"canonical_sha256":"5c2c98ed5091eff05af9a130ec3308fa369f97de7f0f49b72eb63d974f09d88c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:58.250944Z","signature_b64":"4gVBEEl5xP3rQg4JWnLZxbujlapqjItCS/BhkwBzxpU3oZVY0PA9d6DxM5EFz+8EvdR36CZQX0kF/FXB7cedDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c2c98ed5091eff05af9a130ec3308fa369f97de7f0f49b72eb63d974f09d88c","last_reissued_at":"2026-05-17T23:41:58.250360Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:58.250360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.01852","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":"2026-05-17T23:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K7vC2wSsJ4Z85kaAQJH1tSKJB2oSkBirgR6LiIuwJB3HPCy7kcOynydCQqqPOWT8x+tGMyrhJQzBm6FZ+jrSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T18:08:38.177642Z"},"content_sha256":"83f9b6c3813b3ca86a0dfa83f21b674e154bc90563863b9826d5890d29a0a6a3","schema_version":"1.0","event_id":"sha256:83f9b6c3813b3ca86a0dfa83f21b674e154bc90563863b9826d5890d29a0a6a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LQWJR3KQSHX7AWXZUEYOYMYI7I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Correlated time-changed L\\'evy Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hasan Fallahgoul, Kihun Nam","submitted_at":"2018-08-06T12:40:07Z","abstract_excerpt":"Carr and Wu (2004), henceforth CW, developed a framework that encompasses almost all of the continuous-time models proposed in the option pricing literature. Their main result hinges on the stopping time property of the time changes, but all of the models CW proposed for the time changes do not satisfy this assumption. In this paper, when the time changes are adapted, but not necessarily stopping times, we provide analogous results to CW. We show that our approach can be applied to all models in CW."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01852","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":"2026-05-17T23:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rX8GwIooSzkZ/Iq70ypGR9NzqzMcffZsQ3oodN3/wa2wPDTbKv2QdBzicHk3y9GaCwWw9QuUSqy4JXqvL4DrAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T18:08:38.177973Z"},"content_sha256":"7b4e52c9c69d5842c5b0cb7f3d228b1eae05c131adc40baf46895e0cae7daa7d","schema_version":"1.0","event_id":"sha256:7b4e52c9c69d5842c5b0cb7f3d228b1eae05c131adc40baf46895e0cae7daa7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LQWJR3KQSHX7AWXZUEYOYMYI7I/bundle.json","state_url":"https://pith.science/pith/LQWJR3KQSHX7AWXZUEYOYMYI7I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LQWJR3KQSHX7AWXZUEYOYMYI7I/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":"2026-06-28T18:08:38Z","links":{"resolver":"https://pith.science/pith/LQWJR3KQSHX7AWXZUEYOYMYI7I","bundle":"https://pith.science/pith/LQWJR3KQSHX7AWXZUEYOYMYI7I/bundle.json","state":"https://pith.science/pith/LQWJR3KQSHX7AWXZUEYOYMYI7I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LQWJR3KQSHX7AWXZUEYOYMYI7I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LQWJR3KQSHX7AWXZUEYOYMYI7I","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":"0115065419a506d8d7644a8caca02b8719d3718c5e9a33f4a2df85e7820981dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-06T12:40:07Z","title_canon_sha256":"2bf11fb3d682d5d5c0aff75f93151c0a83fec693138cc3055c8692b6a9826bd3"},"schema_version":"1.0","source":{"id":"1808.01852","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01852","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01852v2","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01852","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"LQWJR3KQSHX7","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LQWJR3KQSHX7AWXZ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LQWJR3KQ","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:7b4e52c9c69d5842c5b0cb7f3d228b1eae05c131adc40baf46895e0cae7daa7d","target":"graph","created_at":"2026-05-17T23:41:58Z","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":"Carr and Wu (2004), henceforth CW, developed a framework that encompasses almost all of the continuous-time models proposed in the option pricing literature. Their main result hinges on the stopping time property of the time changes, but all of the models CW proposed for the time changes do not satisfy this assumption. In this paper, when the time changes are adapted, but not necessarily stopping times, we provide analogous results to CW. We show that our approach can be applied to all models in CW.","authors_text":"Hasan Fallahgoul, Kihun Nam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-06T12:40:07Z","title":"Correlated time-changed L\\'evy Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01852","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":"sha256:83f9b6c3813b3ca86a0dfa83f21b674e154bc90563863b9826d5890d29a0a6a3","target":"record","created_at":"2026-05-17T23:41:58Z","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":"0115065419a506d8d7644a8caca02b8719d3718c5e9a33f4a2df85e7820981dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-06T12:40:07Z","title_canon_sha256":"2bf11fb3d682d5d5c0aff75f93151c0a83fec693138cc3055c8692b6a9826bd3"},"schema_version":"1.0","source":{"id":"1808.01852","kind":"arxiv","version":2}},"canonical_sha256":"5c2c98ed5091eff05af9a130ec3308fa369f97de7f0f49b72eb63d974f09d88c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c2c98ed5091eff05af9a130ec3308fa369f97de7f0f49b72eb63d974f09d88c","first_computed_at":"2026-05-17T23:41:58.250360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:58.250360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4gVBEEl5xP3rQg4JWnLZxbujlapqjItCS/BhkwBzxpU3oZVY0PA9d6DxM5EFz+8EvdR36CZQX0kF/FXB7cedDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:58.250944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01852","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83f9b6c3813b3ca86a0dfa83f21b674e154bc90563863b9826d5890d29a0a6a3","sha256:7b4e52c9c69d5842c5b0cb7f3d228b1eae05c131adc40baf46895e0cae7daa7d"],"state_sha256":"a649ab1644d20ed5b6b11fc4140d6db175aa76d21a461bb9371f1f934c103495"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aEGF3oItwmgfd40/aUre7MbIJpOJ5ckTNO0cMgUuUhe0dX9sF/mI20u7IhluTG2SBiKtdGJ27CRdRIyZ/FomDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T18:08:38.180170Z","bundle_sha256":"02ee66837627c2f33dc7fffdf25f6d3a618a1879dae3603823736e46d1ca3f46"}}