{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:4RR4DCL3Y4YGMVHR4BJVEKZSB2","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":"f5be32e61c5a630ced250295924a90128ffc4f32ff1e06a963a7d7b629b84403","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-02T06:30:44Z","title_canon_sha256":"91f9d464036ca2fc563b425a34a305b74ddbedbeebe1bd38a27460ca17abac2a"},"schema_version":"1.0","source":{"id":"0907.0292","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0292","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0292v1","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0292","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"4RR4DCL3Y4YG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4RR4DCL3Y4YGMVHR","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4RR4DCL3","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:f497a3d5bcb891109bf1e0512e3b846526877b5cb71bf233ea1362325d8e994f","target":"graph","created_at":"2026-05-18T04:40:54Z","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":"By using Malliavin calculus and multiple Wiener-It\\^o integrals, we study the existence and the regularity of stochastic currents defined as Skorohod (divergence) integrals with respect to the Brownian motion and to the fractional Brownian motion. We consider also the multidimensional multiparameter case and we compare the regularity of the current as a distribution in negative Sobolev spaces with its regularity in Watanabe space.","authors_text":"Ciprian Tudor (CES, Franco Flandoli, Samos)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-02T06:30:44Z","title":"Brownian and fractional Brownian stochastic currents via Malliavin calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0292","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":"sha256:7ba54c998db00587e3dca8808ae3a0d1f39006cc01603cdbc8ba69c03a50df82","target":"record","created_at":"2026-05-18T04:40:54Z","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":"f5be32e61c5a630ced250295924a90128ffc4f32ff1e06a963a7d7b629b84403","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-07-02T06:30:44Z","title_canon_sha256":"91f9d464036ca2fc563b425a34a305b74ddbedbeebe1bd38a27460ca17abac2a"},"schema_version":"1.0","source":{"id":"0907.0292","kind":"arxiv","version":1}},"canonical_sha256":"e463c1897bc7306654f1e053522b320e9416d197cb7a994519ac9981fbea611f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e463c1897bc7306654f1e053522b320e9416d197cb7a994519ac9981fbea611f","first_computed_at":"2026-05-18T04:40:54.669929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:54.669929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3+TGFIPdXjsPV8Fha882/xhupnG4luUPlHV5kfNcam7yRTUqyP3ntF57Z96ljMPy419HhTVrkx4JS0KTYw4FBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:54.670462Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0292","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ba54c998db00587e3dca8808ae3a0d1f39006cc01603cdbc8ba69c03a50df82","sha256:f497a3d5bcb891109bf1e0512e3b846526877b5cb71bf233ea1362325d8e994f"],"state_sha256":"128ca26fcd0390eec5e4c3696a8996b89f8e0779fa29dddd4963f05afaca885a"}