{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VQTEULBQHXODNPHEVFNURLEKS5","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":"7cbb742894cef0d332d0ec5a168c14e9e58b9eb141bd6f75abd38c02fea36e7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-23T17:10:11Z","title_canon_sha256":"b4d69efe6c0caa80ccf61450cf6ef8380e6907e44d95f9dcfe48cdc5926f287d"},"schema_version":"1.0","source":{"id":"1206.5415","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5415","created_at":"2026-05-18T02:25:32Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5415v2","created_at":"2026-05-18T02:25:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5415","created_at":"2026-05-18T02:25:32Z"},{"alias_kind":"pith_short_12","alias_value":"VQTEULBQHXOD","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VQTEULBQHXODNPHE","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VQTEULBQ","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:dafb8393c3e7bff7866aa2fe2f6dde17a3d1cb06cf9900c471eed87e96271608","target":"graph","created_at":"2026-05-18T02:25:32Z","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 Gaussian Besov spaces obtained by real interpolation and Riemann-Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension. The results are applied to study an approximation problem in $L_p$ for $2\\le p<\\infty$ for stochastic integrals with respect to the $d$-dimensional (geometric) Brownian motion.","authors_text":"Anni Toivola, Stefan Geiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-23T17:10:11Z","title":"On fractional smoothness and $L_p$-approximation on the Gaussian space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5415","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:ab676fd7fc9e917e9ddddd1ced4e7b964e088d581c1ee25e6f5118ecd96c1f74","target":"record","created_at":"2026-05-18T02:25:32Z","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":"7cbb742894cef0d332d0ec5a168c14e9e58b9eb141bd6f75abd38c02fea36e7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-23T17:10:11Z","title_canon_sha256":"b4d69efe6c0caa80ccf61450cf6ef8380e6907e44d95f9dcfe48cdc5926f287d"},"schema_version":"1.0","source":{"id":"1206.5415","kind":"arxiv","version":2}},"canonical_sha256":"ac264a2c303ddc36bce4a95b48ac8a97450cec71129863cff4e9050e9ffc9023","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac264a2c303ddc36bce4a95b48ac8a97450cec71129863cff4e9050e9ffc9023","first_computed_at":"2026-05-18T02:25:32.908040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:32.908040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xd1wrHpqbzJZfolxxGyyurDxIkMuUwq8/3Dx6UjQGFtaQYw97NUNGrKgnB11iLOX7xYOAyrOES8PKb+1Hf86Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:32.908449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5415","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab676fd7fc9e917e9ddddd1ced4e7b964e088d581c1ee25e6f5118ecd96c1f74","sha256:dafb8393c3e7bff7866aa2fe2f6dde17a3d1cb06cf9900c471eed87e96271608"],"state_sha256":"3206443992ef504b7882d0f1596216191ee20a55066efa791eb3e66d4e5be1a8"}