{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NWKHJXYFJEDJJ7W6L76Z3IOXL4","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":"10a205c2a34555251c795e3086b77207c709ed040c71dc100fb0c7122ccde5ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-15T16:08:20Z","title_canon_sha256":"49e7ac86db99f508c2810c2bff41b8c68ae1f9e29154fc61f950eedbe620e21f"},"schema_version":"1.0","source":{"id":"1603.04735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04735","created_at":"2026-05-18T01:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04735v1","created_at":"2026-05-18T01:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04735","created_at":"2026-05-18T01:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"NWKHJXYFJEDJ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NWKHJXYFJEDJJ7W6","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NWKHJXYF","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:df1eb851aa324dc276ee07abd9ee5df3013d3d58a5071329d98272041dd4c5a3","target":"graph","created_at":"2026-05-18T01:19:04Z","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 consider a Brownian functional $F=g\\bigl(\\int_0^T \\eta(s) dW_s\\bigr)$ with $g \\in L_2(\\gamma)$ and a singular deterministic $\\eta$. We deduce the $L_2$-convergence rate for the approximation $F^{(n)} = E F + \\int_0^T \\phi^{(n)}(s) dW_s$ for a class of piecewise constant predictable integrands $\\phi^{(n)}$ from the fractional smoothness of $g$ quantified by Besov spaces and the rate of singularity of $\\eta$.","authors_text":"Anni Laitinen, Dario Gasbarra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-15T16:08:20Z","title":"Convergence rate for the hedging error of a path-dependent example"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04735","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":"sha256:0be57c48b8ae064c738914200334644d7a9ef3fa788f4867563fc752b7b5a4c5","target":"record","created_at":"2026-05-18T01:19:04Z","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":"10a205c2a34555251c795e3086b77207c709ed040c71dc100fb0c7122ccde5ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-15T16:08:20Z","title_canon_sha256":"49e7ac86db99f508c2810c2bff41b8c68ae1f9e29154fc61f950eedbe620e21f"},"schema_version":"1.0","source":{"id":"1603.04735","kind":"arxiv","version":1}},"canonical_sha256":"6d9474df05490694fede5ffd9da1d75f3a2debbff2344db95ed7b5af06696214","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d9474df05490694fede5ffd9da1d75f3a2debbff2344db95ed7b5af06696214","first_computed_at":"2026-05-18T01:19:04.099616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:04.099616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xj5dA/1SMLqt6ntAdD7WiLS1dculnBN080e4k1lhAxVT47SdRpXFr5fxdFqlxmZrZgrx7ayLKupe23P2PlVPAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:04.100162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0be57c48b8ae064c738914200334644d7a9ef3fa788f4867563fc752b7b5a4c5","sha256:df1eb851aa324dc276ee07abd9ee5df3013d3d58a5071329d98272041dd4c5a3"],"state_sha256":"7378da4b7676bf5178a3c5f0a4fcaed8fa00f9c4a1909ed705c42b268e973f2a"}