{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:J43K72CJAWKWXOXF22F3C7W2JD","short_pith_number":"pith:J43K72CJ","schema_version":"1.0","canonical_sha256":"4f36afe84905956bbae5d68bb17eda48f6fe00a210495af9d7c9593768a031d1","source":{"kind":"arxiv","id":"1405.5713","version":4},"attestation_state":"computed","paper":{"title":"Spectral tensor-train decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Allan P. Engsig-Karup, Daniele Bigoni, Youssef M. Marzouk","submitted_at":"2014-05-22T11:22:24Z","abstract_excerpt":"The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT decomposition and analyze its properties. We obtain results on the convergence of the decomposition, revealing links between the regularity of the function, the dimension of the input space, and the TT ranks. We also show that the regularity of the target function is preserved by the univariate functions"},"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":"1405.5713","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-22T11:22:24Z","cross_cats_sorted":[],"title_canon_sha256":"54bd5c8e2f55e686998eb8a6ed5fe6b00dcbb6d0162bc914f597b28334d9efc3","abstract_canon_sha256":"c2ce319f3e6e018c39c0a6a2ce910cd218a22a374034046e153b2d0582b3cf28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:30.479355Z","signature_b64":"XLZiDaLYrzss3KefSiIhEM6Lx1GZrQHnl0eAaYzkEixCryyc84qHd7bwRce43XFhqEf14PXEfdGnt1dIje2XDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f36afe84905956bbae5d68bb17eda48f6fe00a210495af9d7c9593768a031d1","last_reissued_at":"2026-05-18T01:04:30.478765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:30.478765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral tensor-train decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Allan P. Engsig-Karup, Daniele Bigoni, Youssef M. Marzouk","submitted_at":"2014-05-22T11:22:24Z","abstract_excerpt":"The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT decomposition and analyze its properties. We obtain results on the convergence of the decomposition, revealing links between the regularity of the function, the dimension of the input space, and the TT ranks. We also show that the regularity of the target function is preserved by the univariate functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5713","kind":"arxiv","version":4},"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":"1405.5713","created_at":"2026-05-18T01:04:30.478847+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.5713v4","created_at":"2026-05-18T01:04:30.478847+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5713","created_at":"2026-05-18T01:04:30.478847+00:00"},{"alias_kind":"pith_short_12","alias_value":"J43K72CJAWKW","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"J43K72CJAWKWXOXF","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"J43K72CJ","created_at":"2026-05-18T12:28:33.132498+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/J43K72CJAWKWXOXF22F3C7W2JD","json":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD.json","graph_json":"https://pith.science/api/pith-number/J43K72CJAWKWXOXF22F3C7W2JD/graph.json","events_json":"https://pith.science/api/pith-number/J43K72CJAWKWXOXF22F3C7W2JD/events.json","paper":"https://pith.science/paper/J43K72CJ"},"agent_actions":{"view_html":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD","download_json":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD.json","view_paper":"https://pith.science/paper/J43K72CJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.5713&json=true","fetch_graph":"https://pith.science/api/pith-number/J43K72CJAWKWXOXF22F3C7W2JD/graph.json","fetch_events":"https://pith.science/api/pith-number/J43K72CJAWKWXOXF22F3C7W2JD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD/action/storage_attestation","attest_author":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD/action/author_attestation","sign_citation":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD/action/citation_signature","submit_replication":"https://pith.science/pith/J43K72CJAWKWXOXF22F3C7W2JD/action/replication_record"}},"created_at":"2026-05-18T01:04:30.478847+00:00","updated_at":"2026-05-18T01:04:30.478847+00:00"}