{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YBOIN5FKFVSW6HQEP5XGNDEV77","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":"9c322f17fcfc5a616a8f942b8c69141496c2c15e650ff3fccdfa9a69ed6b5707","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-23T13:32:36Z","title_canon_sha256":"731eeb0e3f85fdf6f647ca7b48c618236c1b8eab6c304ac184dfe8437f7172a4"},"schema_version":"1.0","source":{"id":"1109.5071","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5071","created_at":"2026-05-18T04:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5071v2","created_at":"2026-05-18T04:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5071","created_at":"2026-05-18T04:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"YBOIN5FKFVSW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YBOIN5FKFVSW6HQE","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YBOIN5FK","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:3377f2ed8a75b15aec087cc128266a6099a874183dae539a8c27598d55365866","target":"graph","created_at":"2026-05-18T04:11:51Z","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 prove an extension of the Ocone-Karatzas integral representation, valid for all $BV$ functions on the classical Wiener space. We establish also an elementary chain rule formula and combine the two results to compute explicit integral representations for some classes of $BV$ composite random variables.","authors_text":"Dario Trevisan, Maurizio Pratelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-23T13:32:36Z","title":"Functions of Bounded Variation on the Classical Wiener Space and an Extended Ocone-Karatzas Formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5071","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":"sha256:863f850f113edd2292fca62333ee75625d2a380accae09acbbbae5133401dd1a","target":"record","created_at":"2026-05-18T04:11:51Z","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":"9c322f17fcfc5a616a8f942b8c69141496c2c15e650ff3fccdfa9a69ed6b5707","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-23T13:32:36Z","title_canon_sha256":"731eeb0e3f85fdf6f647ca7b48c618236c1b8eab6c304ac184dfe8437f7172a4"},"schema_version":"1.0","source":{"id":"1109.5071","kind":"arxiv","version":2}},"canonical_sha256":"c05c86f4aa2d656f1e047f6e668c95ffcd31432fc99fd01eebe4c54a20849cdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c05c86f4aa2d656f1e047f6e668c95ffcd31432fc99fd01eebe4c54a20849cdd","first_computed_at":"2026-05-18T04:11:51.153078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:51.153078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e0Y/GzpwkhS1j9LRJQIEBf9fOHIn+Jj84Bj3IV1mkgy33bdjrSgvP1hxHhe+Eu/3NFE84iqm0VyoENjWxLKnAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:51.153664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5071","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:863f850f113edd2292fca62333ee75625d2a380accae09acbbbae5133401dd1a","sha256:3377f2ed8a75b15aec087cc128266a6099a874183dae539a8c27598d55365866"],"state_sha256":"abc1d07a40687833dc41c2b2f0536b2eec1725ac8be62de6979087c48d3ac0f7"}