{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZTW227YNBS6ZHGW52TYSMHWKIL","short_pith_number":"pith:ZTW227YN","canonical_record":{"source":{"id":"1701.01085","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-04T17:33:08Z","cross_cats_sorted":[],"title_canon_sha256":"744638c0f49a5e1f6873986ddfa3154db7f81a0d71cb92f173da1327a2b54bad","abstract_canon_sha256":"6d38a59200d4df7cbcbd86af29b7184c472caf99e197ecd8adeec425c3e92506"},"schema_version":"1.0"},"canonical_sha256":"ccedad7f0d0cbd939addd4f1261eca42f3165d7bb61e8d02f8e74effe1cc219d","source":{"kind":"arxiv","id":"1701.01085","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01085","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01085v4","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01085","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZTW227YNBS6Z","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZTW227YNBS6ZHGW5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZTW227YN","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZTW227YNBS6ZHGW52TYSMHWKIL","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01085","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-04T17:33:08Z","cross_cats_sorted":[],"title_canon_sha256":"744638c0f49a5e1f6873986ddfa3154db7f81a0d71cb92f173da1327a2b54bad","abstract_canon_sha256":"6d38a59200d4df7cbcbd86af29b7184c472caf99e197ecd8adeec425c3e92506"},"schema_version":"1.0"},"canonical_sha256":"ccedad7f0d0cbd939addd4f1261eca42f3165d7bb61e8d02f8e74effe1cc219d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:39.833079Z","signature_b64":"Voi5iTfpdxY+S1Rjkr7h/XIH1Wzd26HQeah7NXYqOeRwIfIbG5vdgesgTb72HfeCxwVL4EDS5FrLR0/8KpVuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccedad7f0d0cbd939addd4f1261eca42f3165d7bb61e8d02f8e74effe1cc219d","last_reissued_at":"2026-05-18T00:24:39.832577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:39.832577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01085","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6KBnkapmiyEWcFcW0Ok4/Df7zp9L+TU/MyfqEAZaSLTREziS1q9Wnct69Z/jrhTJZi7LMXwZYE7x4KVTGIoUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:52:40.232757Z"},"content_sha256":"3c49fc09b235d53adfe2258be2e9415c1b3c23393f8c7e5fd10a1f6dc3494e65","schema_version":"1.0","event_id":"sha256:3c49fc09b235d53adfe2258be2e9415c1b3c23393f8c7e5fd10a1f6dc3494e65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZTW227YNBS6ZHGW52TYSMHWKIL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusion transformations, Black-Scholes equation and optimal stopping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Umut \\c{C}etin","submitted_at":"2017-01-04T17:33:08Z","abstract_excerpt":"We develop a new class of path transformations for one-dimensional diffusions that are tailored to alter their long-run behaviour from transient to recurrent or vice versa. This immediately leads to a formula for the distribution of the first exit times of diffusions, which is recently characterised by Karatzas and Ruf \\cite{KR} as the minimal solution of an appropriate Cauchy problem under more stringent conditions. A particular limit of these transformations also turn out to be instrumental in characterising the stochastic solutions of Cauchy problems defined by the generators of strict loca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01085","kind":"arxiv","version":4},"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":"2026-05-18T00:24:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fcTPMW4pZ+CThQMQbDSN19K1w6MWeMzIX6GXufqpF4HjLmqyeyFfsnAOg5pBUYpSkh0NbS242A5NgYnHxLq5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:52:40.233099Z"},"content_sha256":"aa993061d6710580e6d7ca5e39c96a35ef951ca3280169813170ddfb5ed51005","schema_version":"1.0","event_id":"sha256:aa993061d6710580e6d7ca5e39c96a35ef951ca3280169813170ddfb5ed51005"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZTW227YNBS6ZHGW52TYSMHWKIL/bundle.json","state_url":"https://pith.science/pith/ZTW227YNBS6ZHGW52TYSMHWKIL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZTW227YNBS6ZHGW52TYSMHWKIL/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":"2026-06-26T01:52:40Z","links":{"resolver":"https://pith.science/pith/ZTW227YNBS6ZHGW52TYSMHWKIL","bundle":"https://pith.science/pith/ZTW227YNBS6ZHGW52TYSMHWKIL/bundle.json","state":"https://pith.science/pith/ZTW227YNBS6ZHGW52TYSMHWKIL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZTW227YNBS6ZHGW52TYSMHWKIL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZTW227YNBS6ZHGW52TYSMHWKIL","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":"6d38a59200d4df7cbcbd86af29b7184c472caf99e197ecd8adeec425c3e92506","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-04T17:33:08Z","title_canon_sha256":"744638c0f49a5e1f6873986ddfa3154db7f81a0d71cb92f173da1327a2b54bad"},"schema_version":"1.0","source":{"id":"1701.01085","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01085","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01085v4","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01085","created_at":"2026-05-18T00:24:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZTW227YNBS6Z","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZTW227YNBS6ZHGW5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZTW227YN","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:aa993061d6710580e6d7ca5e39c96a35ef951ca3280169813170ddfb5ed51005","target":"graph","created_at":"2026-05-18T00:24:39Z","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 develop a new class of path transformations for one-dimensional diffusions that are tailored to alter their long-run behaviour from transient to recurrent or vice versa. This immediately leads to a formula for the distribution of the first exit times of diffusions, which is recently characterised by Karatzas and Ruf \\cite{KR} as the minimal solution of an appropriate Cauchy problem under more stringent conditions. A particular limit of these transformations also turn out to be instrumental in characterising the stochastic solutions of Cauchy problems defined by the generators of strict loca","authors_text":"Umut \\c{C}etin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-04T17:33:08Z","title":"Diffusion transformations, Black-Scholes equation and optimal stopping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01085","kind":"arxiv","version":4},"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":"sha256:3c49fc09b235d53adfe2258be2e9415c1b3c23393f8c7e5fd10a1f6dc3494e65","target":"record","created_at":"2026-05-18T00:24:39Z","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":"6d38a59200d4df7cbcbd86af29b7184c472caf99e197ecd8adeec425c3e92506","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-04T17:33:08Z","title_canon_sha256":"744638c0f49a5e1f6873986ddfa3154db7f81a0d71cb92f173da1327a2b54bad"},"schema_version":"1.0","source":{"id":"1701.01085","kind":"arxiv","version":4}},"canonical_sha256":"ccedad7f0d0cbd939addd4f1261eca42f3165d7bb61e8d02f8e74effe1cc219d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccedad7f0d0cbd939addd4f1261eca42f3165d7bb61e8d02f8e74effe1cc219d","first_computed_at":"2026-05-18T00:24:39.832577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:39.832577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Voi5iTfpdxY+S1Rjkr7h/XIH1Wzd26HQeah7NXYqOeRwIfIbG5vdgesgTb72HfeCxwVL4EDS5FrLR0/8KpVuDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:39.833079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01085","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c49fc09b235d53adfe2258be2e9415c1b3c23393f8c7e5fd10a1f6dc3494e65","sha256:aa993061d6710580e6d7ca5e39c96a35ef951ca3280169813170ddfb5ed51005"],"state_sha256":"d6eb03a7112ad31c4e08725365d56432ac3cd8ef9de58170c1e4dc6558e425bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2U3dz0O5dwF4IbKFdHjcDcBPBjJP93GJUzIS165TVOJWPBKUtEMjR/hJYLz0fmi63WDG+jDw/UhI80MmHLikBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:52:40.235192Z","bundle_sha256":"21aefc535097c84cdbb69b7deb990b1624be1cf94f9e96398bb9b30d9f8f9a46"}}