{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XK6Y36ULJM44XTQHBTJP465HCC","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":"c44c19f796d066cf6475305afffa0c2a5199c16f8a0322a0b568684b14ef2d48","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-16T20:44:33Z","title_canon_sha256":"305a5d78aea90d452a77924fa5fab111ea36669548abbdd0bbbf7296b07c1bbf"},"schema_version":"1.0","source":{"id":"1210.4572","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4572","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4572v1","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4572","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"pith_short_12","alias_value":"XK6Y36ULJM44","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XK6Y36ULJM44XTQH","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XK6Y36UL","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:ccbdd12a3f71285ef1e3190b27545f41a5ba9338f49a0aca41f7f0cb20c7a54d","target":"graph","created_at":"2026-05-18T03:42:56Z","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":"Let $v:[0,T]\\times \\R^d \\to \\R$ be the solution of the parabolic backward equation $ \\partial_t v + (1/2) \\sum_{i,l} [\\sigma \\sigma^\\perp]_{il} \\partial_{x_i \\partial_{x_l} v + \\sum_{i} b_i \\partial_{x_i}v + kv =0$ with terminal condition $g$, where the coefficients are time- and state-dependent, and satisfy certain regularity assumptions. Let $X=(X_t)_{t\\in [0,T]}$ be the associated $\\R^d$-valued diffusion process on some appropriate $(\\Omega,\\cF,\\Q)$. For $p\\in [2,\\infty)$ and a measure $d\\P=\\lambda_T d\\Q$, where $\\lambda_T$ satisfies the Muckenhoupt condition $A_\\alpha$ for $\\alpha \\in (1,p","authors_text":"Emmanuel Gobet, Stefan Geiss","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-16T20:44:33Z","title":"Fractional smoothness of functionals of diffusion processes under a change of measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4572","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":"sha256:40eb10813cbb1bbfcfd8069d5c443a827c51400ae8d8e1ae6759c954a77f5c47","target":"record","created_at":"2026-05-18T03:42:56Z","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":"c44c19f796d066cf6475305afffa0c2a5199c16f8a0322a0b568684b14ef2d48","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-16T20:44:33Z","title_canon_sha256":"305a5d78aea90d452a77924fa5fab111ea36669548abbdd0bbbf7296b07c1bbf"},"schema_version":"1.0","source":{"id":"1210.4572","kind":"arxiv","version":1}},"canonical_sha256":"babd8dfa8b4b39cbce070cd2fe7ba710b7c947588c93ab1a42e83be4dec3f9b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"babd8dfa8b4b39cbce070cd2fe7ba710b7c947588c93ab1a42e83be4dec3f9b2","first_computed_at":"2026-05-18T03:42:56.709975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:56.709975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6GzVFNWML4LkwZrxV4Gkboz8c2PNMxHH4InFbS4RLpZnu6pxvobEXZ+ukJ3Bk0voUTSiMyvgGSzI81cO+Y64AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:56.710626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4572","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40eb10813cbb1bbfcfd8069d5c443a827c51400ae8d8e1ae6759c954a77f5c47","sha256:ccbdd12a3f71285ef1e3190b27545f41a5ba9338f49a0aca41f7f0cb20c7a54d"],"state_sha256":"4364058f1ccfabf2f6f67825b578204a3d7f71af43553b11166ccb5b34173269"}