{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JINUOESDSKLC66XC7DXJGGJX4N","short_pith_number":"pith:JINUOESD","schema_version":"1.0","canonical_sha256":"4a1b47124392962f7ae2f8ee931937e3488f0405bcb3552c7d232b23bc45104e","source":{"kind":"arxiv","id":"1505.03225","version":1},"attestation_state":"computed","paper":{"title":"An optimal approximation of Rosenblatt sheet by multiple Wiener integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guangjun Shen, Qian Yu","submitted_at":"2015-05-13T02:59:37Z","abstract_excerpt":"Let $Z^{\\alpha,\\beta}$ be the Rosenblatt sheet with the representation $$ Z^{\\alpha,\\beta}(t,s)=\\int^t_0\\int^s_0\\int^t_0\\int^s_0Q^\\alpha(t,y_1,y_2)Q^\\beta(s,u_1,u_2)B(dy_1,du_1)B(dy_2,du_2) $$ where $B$ is a Brownian sheet, $\\frac12<\\alpha,\\beta<1$, $Q^\\alpha$ and $Q^\\beta$ are the given kernel. In this paper, we contruct multiple Wiener integrals of the form \\begin{align*} \\int^t_0\\int^s_0\\int^t_0\\int^s_0&[k_1(y_1,y_2)^{-\\frac12\\alpha}(u_1,u_2)^{-\\frac12\\beta}+k_2(y_1\\vee y_2)^{\\frac12\\alpha}(y_1\\wedge y_2)^{-\\frac12\\alpha}|y_1-y_2|^{\\alpha-1}\\\\ &\\cdot(u_1\\vee u_2)^{\\frac12\\beta}(u_1\\wedge u_"},"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":"1505.03225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-13T02:59:37Z","cross_cats_sorted":[],"title_canon_sha256":"eb887d605802c4d6f59cb8b5a9487aa9b642b954f98e9f4df635e398733516d8","abstract_canon_sha256":"a31e659b3ddbda4bde7162024c338948161e61078b7d602fd6910cb6bbfa1402"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:10.007476Z","signature_b64":"i+Mu4qw34WHa0dPimsovN9rW5HGCKvRBM9KMzUJ7yIozjGTnd8M0YIkMmLUcozghOZQnhUG+YyzBfe6mvCtPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a1b47124392962f7ae2f8ee931937e3488f0405bcb3552c7d232b23bc45104e","last_reissued_at":"2026-05-18T02:12:10.006142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:10.006142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An optimal approximation of Rosenblatt sheet by multiple Wiener integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guangjun Shen, Qian Yu","submitted_at":"2015-05-13T02:59:37Z","abstract_excerpt":"Let $Z^{\\alpha,\\beta}$ be the Rosenblatt sheet with the representation $$ Z^{\\alpha,\\beta}(t,s)=\\int^t_0\\int^s_0\\int^t_0\\int^s_0Q^\\alpha(t,y_1,y_2)Q^\\beta(s,u_1,u_2)B(dy_1,du_1)B(dy_2,du_2) $$ where $B$ is a Brownian sheet, $\\frac12<\\alpha,\\beta<1$, $Q^\\alpha$ and $Q^\\beta$ are the given kernel. In this paper, we contruct multiple Wiener integrals of the form \\begin{align*} \\int^t_0\\int^s_0\\int^t_0\\int^s_0&[k_1(y_1,y_2)^{-\\frac12\\alpha}(u_1,u_2)^{-\\frac12\\beta}+k_2(y_1\\vee y_2)^{\\frac12\\alpha}(y_1\\wedge y_2)^{-\\frac12\\alpha}|y_1-y_2|^{\\alpha-1}\\\\ &\\cdot(u_1\\vee u_2)^{\\frac12\\beta}(u_1\\wedge u_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03225","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":"1505.03225","created_at":"2026-05-18T02:12:10.006234+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.03225v1","created_at":"2026-05-18T02:12:10.006234+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03225","created_at":"2026-05-18T02:12:10.006234+00:00"},{"alias_kind":"pith_short_12","alias_value":"JINUOESDSKLC","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JINUOESDSKLC66XC","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JINUOESD","created_at":"2026-05-18T12:29:27.538025+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/JINUOESDSKLC66XC7DXJGGJX4N","json":"https://pith.science/pith/JINUOESDSKLC66XC7DXJGGJX4N.json","graph_json":"https://pith.science/api/pith-number/JINUOESDSKLC66XC7DXJGGJX4N/graph.json","events_json":"https://pith.science/api/pith-number/JINUOESDSKLC66XC7DXJGGJX4N/events.json","paper":"https://pith.science/paper/JINUOESD"},"agent_actions":{"view_html":"https://pith.science/pith/JINUOESDSKLC66XC7DXJGGJX4N","download_json":"https://pith.science/pith/JINUOESDSKLC66XC7DXJGGJX4N.json","view_paper":"https://pith.science/paper/JINUOESD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.03225&json=true","fetch_graph":"https://pith.science/api/pith-number/JINUOESDSKLC66XC7DXJGGJX4N/graph.json","fetch_events":"https://pith.science/api/pith-number/JINUOESDSKLC66XC7DXJGGJX4N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JINUOESDSKLC66XC7DXJGGJX4N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JINUOESDSKLC66XC7DXJGGJX4N/action/storage_attestation","attest_author":"https://pith.science/pith/JINUOESDSKLC66XC7DXJGGJX4N/action/author_attestation","sign_citation":"https://pith.science/pith/JINUOESDSKLC66XC7DXJGGJX4N/action/citation_signature","submit_replication":"https://pith.science/pith/JINUOESDSKLC66XC7DXJGGJX4N/action/replication_record"}},"created_at":"2026-05-18T02:12:10.006234+00:00","updated_at":"2026-05-18T02:12:10.006234+00:00"}