{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MTJHAOYDD6LWS4QWZEE5N4MJDY","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":"41f30a71fb00fd8bf157c2976aab3855fdd0603c29590b355187fb0a886a3d1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T13:23:19Z","title_canon_sha256":"8216bcd1e5f4e72dfffa2f39141f9d77be45ba0d34e5a83d96564032a10f64c9"},"schema_version":"1.0","source":{"id":"1609.07352","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07352","created_at":"2026-05-18T00:30:22Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07352v3","created_at":"2026-05-18T00:30:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07352","created_at":"2026-05-18T00:30:22Z"},{"alias_kind":"pith_short_12","alias_value":"MTJHAOYDD6LW","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTJHAOYDD6LWS4QW","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTJHAOYD","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:4b0319da223640d41bd3182fa7b1406066400cc2eb19fc723f12dc83c8127c5f","target":"graph","created_at":"2026-05-18T00:30:22Z","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":"In this work we present different results concerning the signature and the cubature of fractional Brownian motion (fBm). The first result regards the rate of convergence of the expected signature of the linear piecewise approximation of the fBm to its exact value, for a value of the Hurst parameter $H\\in(\\frac{1}{2},1)$. We show that the rate of convergence is given by $2H$. We believe that this rate is sharp as it is consistent with the result of Ni and Xu, who showed that the sharp rate of convergence for the Brownian motion (i.e. fBm with $H=\\frac{1}{2}$) is given by $1$. The second result ","authors_text":"Riccardo Passeggeri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T13:23:19Z","title":"Some results on the Signature and Cubature of the Fractional Brownian motion for $H>\\frac{1}{2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07352","kind":"arxiv","version":3},"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":"sha256:06ba43bd837a78b3ee5c727fc991f9413ecad045faaf38cbeb815d59e6e510a9","target":"record","created_at":"2026-05-18T00:30:22Z","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":"41f30a71fb00fd8bf157c2976aab3855fdd0603c29590b355187fb0a886a3d1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T13:23:19Z","title_canon_sha256":"8216bcd1e5f4e72dfffa2f39141f9d77be45ba0d34e5a83d96564032a10f64c9"},"schema_version":"1.0","source":{"id":"1609.07352","kind":"arxiv","version":3}},"canonical_sha256":"64d2703b031f97697216c909d6f1891e163954b962d64e59d1c54f319b07073f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64d2703b031f97697216c909d6f1891e163954b962d64e59d1c54f319b07073f","first_computed_at":"2026-05-18T00:30:22.548835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:22.548835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M91tCWC8PYt1K8h+2MQltTIDC1zJQn2B5EHADE+O8GRAwecQU5jffiCB/zqaKKxXuIFYoythCZ5BfveCfuzTDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:22.549505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07352","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06ba43bd837a78b3ee5c727fc991f9413ecad045faaf38cbeb815d59e6e510a9","sha256:4b0319da223640d41bd3182fa7b1406066400cc2eb19fc723f12dc83c8127c5f"],"state_sha256":"1778f808d3d2972ceaf0850dadb5f98265617c5290769989079ffb82173d2641"}