{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XK6Y36ULJM44XTQHBTJP465HCC","short_pith_number":"pith:XK6Y36UL","schema_version":"1.0","canonical_sha256":"babd8dfa8b4b39cbce070cd2fe7ba710b7c947588c93ab1a42e83be4dec3f9b2","source":{"kind":"arxiv","id":"1210.4572","version":1},"attestation_state":"computed","paper":{"title":"Fractional smoothness of functionals of diffusion processes under a change of measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.PR","authors_text":"Emmanuel Gobet, Stefan Geiss","submitted_at":"2012-10-16T20:44:33Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.4572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-16T20:44:33Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"305a5d78aea90d452a77924fa5fab111ea36669548abbdd0bbbf7296b07c1bbf","abstract_canon_sha256":"c44c19f796d066cf6475305afffa0c2a5199c16f8a0322a0b568684b14ef2d48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:56.710626Z","signature_b64":"6GzVFNWML4LkwZrxV4Gkboz8c2PNMxHH4InFbS4RLpZnu6pxvobEXZ+ukJ3Bk0voUTSiMyvgGSzI81cO+Y64AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"babd8dfa8b4b39cbce070cd2fe7ba710b7c947588c93ab1a42e83be4dec3f9b2","last_reissued_at":"2026-05-18T03:42:56.709975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:56.709975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional smoothness of functionals of diffusion processes under a change of measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.PR","authors_text":"Emmanuel Gobet, Stefan Geiss","submitted_at":"2012-10-16T20:44:33Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4572","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.4572","created_at":"2026-05-18T03:42:56.710077+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.4572v1","created_at":"2026-05-18T03:42:56.710077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4572","created_at":"2026-05-18T03:42:56.710077+00:00"},{"alias_kind":"pith_short_12","alias_value":"XK6Y36ULJM44","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XK6Y36ULJM44XTQH","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XK6Y36UL","created_at":"2026-05-18T12:27:27.928770+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XK6Y36ULJM44XTQHBTJP465HCC","json":"https://pith.science/pith/XK6Y36ULJM44XTQHBTJP465HCC.json","graph_json":"https://pith.science/api/pith-number/XK6Y36ULJM44XTQHBTJP465HCC/graph.json","events_json":"https://pith.science/api/pith-number/XK6Y36ULJM44XTQHBTJP465HCC/events.json","paper":"https://pith.science/paper/XK6Y36UL"},"agent_actions":{"view_html":"https://pith.science/pith/XK6Y36ULJM44XTQHBTJP465HCC","download_json":"https://pith.science/pith/XK6Y36ULJM44XTQHBTJP465HCC.json","view_paper":"https://pith.science/paper/XK6Y36UL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.4572&json=true","fetch_graph":"https://pith.science/api/pith-number/XK6Y36ULJM44XTQHBTJP465HCC/graph.json","fetch_events":"https://pith.science/api/pith-number/XK6Y36ULJM44XTQHBTJP465HCC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XK6Y36ULJM44XTQHBTJP465HCC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XK6Y36ULJM44XTQHBTJP465HCC/action/storage_attestation","attest_author":"https://pith.science/pith/XK6Y36ULJM44XTQHBTJP465HCC/action/author_attestation","sign_citation":"https://pith.science/pith/XK6Y36ULJM44XTQHBTJP465HCC/action/citation_signature","submit_replication":"https://pith.science/pith/XK6Y36ULJM44XTQHBTJP465HCC/action/replication_record"}},"created_at":"2026-05-18T03:42:56.710077+00:00","updated_at":"2026-05-18T03:42:56.710077+00:00"}