{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UBAC7ZEIZ565R5BJWCKIGK52YF","short_pith_number":"pith:UBAC7ZEI","schema_version":"1.0","canonical_sha256":"a0402fe488cf7dd8f429b094832bbac15d488e58355208c3b581a359a2271377","source":{"kind":"arxiv","id":"1505.04639","version":3},"attestation_state":"computed","paper":{"title":"Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Reisinger, Rasmus Wissmann","submitted_at":"2015-05-18T13:49:41Z","abstract_excerpt":"We study an expansion method for high-dimensional parabolic PDEs which constructs accurate approximate solutions by decomposition into solutions to lower-dimensional PDEs, and which is particularly effective if there are a low number of dominant principal components. The focus of the present article is the derivation of sharp error bounds for the constant coefficient case and a first and second order approximation. We give a precise characterisation when these bounds hold for (non-smooth) option pricing applications and provide numerical results demonstrating that the practically observed conv"},"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":"1505.04639","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-18T13:49:41Z","cross_cats_sorted":[],"title_canon_sha256":"4c31ea9e6b3a8e823484b777feb63ba269fc0271c0cfb4446015a73d7eda50f0","abstract_canon_sha256":"ea80b739e1b2845a24cf4a71cc80a582c469d0e5be46b738f5ed6f5d264b9d76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:10.264082Z","signature_b64":"4Hk1IIbNEyT16+A2HKuFadlU525oWdIWe3P6+UITcJdtpRncP1iisr3TxAPltGleiz+Mb71Fx6wwz/QQy8cpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0402fe488cf7dd8f429b094832bbac15d488e58355208c3b581a359a2271377","last_reissued_at":"2026-05-18T01:00:10.263463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:10.263463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Reisinger, Rasmus Wissmann","submitted_at":"2015-05-18T13:49:41Z","abstract_excerpt":"We study an expansion method for high-dimensional parabolic PDEs which constructs accurate approximate solutions by decomposition into solutions to lower-dimensional PDEs, and which is particularly effective if there are a low number of dominant principal components. The focus of the present article is the derivation of sharp error bounds for the constant coefficient case and a first and second order approximation. We give a precise characterisation when these bounds hold for (non-smooth) option pricing applications and provide numerical results demonstrating that the practically observed conv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04639","kind":"arxiv","version":3},"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":"1505.04639","created_at":"2026-05-18T01:00:10.263550+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.04639v3","created_at":"2026-05-18T01:00:10.263550+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04639","created_at":"2026-05-18T01:00:10.263550+00:00"},{"alias_kind":"pith_short_12","alias_value":"UBAC7ZEIZ565","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UBAC7ZEIZ565R5BJ","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UBAC7ZEI","created_at":"2026-05-18T12:29:44.643036+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/UBAC7ZEIZ565R5BJWCKIGK52YF","json":"https://pith.science/pith/UBAC7ZEIZ565R5BJWCKIGK52YF.json","graph_json":"https://pith.science/api/pith-number/UBAC7ZEIZ565R5BJWCKIGK52YF/graph.json","events_json":"https://pith.science/api/pith-number/UBAC7ZEIZ565R5BJWCKIGK52YF/events.json","paper":"https://pith.science/paper/UBAC7ZEI"},"agent_actions":{"view_html":"https://pith.science/pith/UBAC7ZEIZ565R5BJWCKIGK52YF","download_json":"https://pith.science/pith/UBAC7ZEIZ565R5BJWCKIGK52YF.json","view_paper":"https://pith.science/paper/UBAC7ZEI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.04639&json=true","fetch_graph":"https://pith.science/api/pith-number/UBAC7ZEIZ565R5BJWCKIGK52YF/graph.json","fetch_events":"https://pith.science/api/pith-number/UBAC7ZEIZ565R5BJWCKIGK52YF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UBAC7ZEIZ565R5BJWCKIGK52YF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UBAC7ZEIZ565R5BJWCKIGK52YF/action/storage_attestation","attest_author":"https://pith.science/pith/UBAC7ZEIZ565R5BJWCKIGK52YF/action/author_attestation","sign_citation":"https://pith.science/pith/UBAC7ZEIZ565R5BJWCKIGK52YF/action/citation_signature","submit_replication":"https://pith.science/pith/UBAC7ZEIZ565R5BJWCKIGK52YF/action/replication_record"}},"created_at":"2026-05-18T01:00:10.263550+00:00","updated_at":"2026-05-18T01:00:10.263550+00:00"}