{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7NFWS7D6TRCBRTKZERCMBBYCUD","short_pith_number":"pith:7NFWS7D6","schema_version":"1.0","canonical_sha256":"fb4b697c7e9c4418cd592444c08702a0f18f4fdc4865269a3eccd1fe28293e2d","source":{"kind":"arxiv","id":"1707.04972","version":2},"attestation_state":"computed","paper":{"title":"A weak version of path-dependent functional It\\^o calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alberto Ohashi, Alexandre B. Simas, Dorival Le\\~ao","submitted_at":"2017-07-17T00:58:49Z","abstract_excerpt":"We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration that provides a differential structure allowing to describe infinitesimal evolution of Wiener functionals at very small scales. The main novel idea is to compute the \"sensitivities\" of processes, namely derivatives of martingale components and a weak notion of infinitesimal generators, via a finite-dimensional approximation procedure based on controlled inter-arrival times and approximating martingales. The theory comes with convergence results that allow to interpret a large class of Wi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.04972","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-17T00:58:49Z","cross_cats_sorted":[],"title_canon_sha256":"009fbcd18268b973c81b82a9a62041d0ecea24442caefd26ac46957db4915696","abstract_canon_sha256":"cf6f81293083b931bda9b717786bc5f210ffdffadd04de6d56dfdf28f1ef11ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:13.148332Z","signature_b64":"92rD6np1qdFvyPGzq8CZJtZhS0Oeg+c2zYvrrOXdHvtOrV/t6gmsEamN6FiqMiQHPGnu/mJ4KMuDYLFAE3OIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb4b697c7e9c4418cd592444c08702a0f18f4fdc4865269a3eccd1fe28293e2d","last_reissued_at":"2026-05-18T00:29:13.147804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:13.147804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A weak version of path-dependent functional It\\^o calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alberto Ohashi, Alexandre B. Simas, Dorival Le\\~ao","submitted_at":"2017-07-17T00:58:49Z","abstract_excerpt":"We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration that provides a differential structure allowing to describe infinitesimal evolution of Wiener functionals at very small scales. The main novel idea is to compute the \"sensitivities\" of processes, namely derivatives of martingale components and a weak notion of infinitesimal generators, via a finite-dimensional approximation procedure based on controlled inter-arrival times and approximating martingales. The theory comes with convergence results that allow to interpret a large class of Wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04972","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.04972","created_at":"2026-05-18T00:29:13.147891+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.04972v2","created_at":"2026-05-18T00:29:13.147891+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04972","created_at":"2026-05-18T00:29:13.147891+00:00"},{"alias_kind":"pith_short_12","alias_value":"7NFWS7D6TRCB","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7NFWS7D6TRCBRTKZ","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7NFWS7D6","created_at":"2026-05-18T12:31:05.417338+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7NFWS7D6TRCBRTKZERCMBBYCUD","json":"https://pith.science/pith/7NFWS7D6TRCBRTKZERCMBBYCUD.json","graph_json":"https://pith.science/api/pith-number/7NFWS7D6TRCBRTKZERCMBBYCUD/graph.json","events_json":"https://pith.science/api/pith-number/7NFWS7D6TRCBRTKZERCMBBYCUD/events.json","paper":"https://pith.science/paper/7NFWS7D6"},"agent_actions":{"view_html":"https://pith.science/pith/7NFWS7D6TRCBRTKZERCMBBYCUD","download_json":"https://pith.science/pith/7NFWS7D6TRCBRTKZERCMBBYCUD.json","view_paper":"https://pith.science/paper/7NFWS7D6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.04972&json=true","fetch_graph":"https://pith.science/api/pith-number/7NFWS7D6TRCBRTKZERCMBBYCUD/graph.json","fetch_events":"https://pith.science/api/pith-number/7NFWS7D6TRCBRTKZERCMBBYCUD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7NFWS7D6TRCBRTKZERCMBBYCUD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7NFWS7D6TRCBRTKZERCMBBYCUD/action/storage_attestation","attest_author":"https://pith.science/pith/7NFWS7D6TRCBRTKZERCMBBYCUD/action/author_attestation","sign_citation":"https://pith.science/pith/7NFWS7D6TRCBRTKZERCMBBYCUD/action/citation_signature","submit_replication":"https://pith.science/pith/7NFWS7D6TRCBRTKZERCMBBYCUD/action/replication_record"}},"created_at":"2026-05-18T00:29:13.147891+00:00","updated_at":"2026-05-18T00:29:13.147891+00:00"}