{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:H632NTESPKFTV7KG526LTTKKHC","short_pith_number":"pith:H632NTES","schema_version":"1.0","canonical_sha256":"3fb7a6cc927a8b3afd46eebcb9cd4a3886534c16c98649618f8cbc454dd7c985","source":{"kind":"arxiv","id":"1406.7026","version":3},"attestation_state":"computed","paper":{"title":"On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.NA","authors_text":"Andr\\'e Uschmajew, Daniel Kressner","submitted_at":"2014-06-26T20:57:09Z","abstract_excerpt":"Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue problems on Hilbert spaces. Although this question is central to the success of all existing solvers based on low-rank tensor techniques, very few of the results available so far allow to draw meaningful conclusions for higher dimensions. In this work, we develop a constructive framework to study low-rank approximability. One major assumption "},"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":"1406.7026","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-26T20:57:09Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"9b1bb00ca96ad49be005c1c1f7981f118fb53e974511d90ce50edd587a795443","abstract_canon_sha256":"3e581773700f0d419ed427b26e337867ef3ffc41dbc6646231505fec20943562"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:16.865307Z","signature_b64":"9kp/PiKyLytbP4IzDv74lRLalC+piHRD3DVrdzx+7tJGX84p6/LJYTjJlzYvOHBQhngxLqYUSS2aLk8XN+6mBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fb7a6cc927a8b3afd46eebcb9cd4a3886534c16c98649618f8cbc454dd7c985","last_reissued_at":"2026-05-18T01:23:16.864535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:16.864535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.NA","authors_text":"Andr\\'e Uschmajew, Daniel Kressner","submitted_at":"2014-06-26T20:57:09Z","abstract_excerpt":"Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue problems on Hilbert spaces. Although this question is central to the success of all existing solvers based on low-rank tensor techniques, very few of the results available so far allow to draw meaningful conclusions for higher dimensions. In this work, we develop a constructive framework to study low-rank approximability. One major assumption "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7026","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":"1406.7026","created_at":"2026-05-18T01:23:16.864657+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.7026v3","created_at":"2026-05-18T01:23:16.864657+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7026","created_at":"2026-05-18T01:23:16.864657+00:00"},{"alias_kind":"pith_short_12","alias_value":"H632NTESPKFT","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"H632NTESPKFTV7KG","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"H632NTES","created_at":"2026-05-18T12:28:30.664211+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/H632NTESPKFTV7KG526LTTKKHC","json":"https://pith.science/pith/H632NTESPKFTV7KG526LTTKKHC.json","graph_json":"https://pith.science/api/pith-number/H632NTESPKFTV7KG526LTTKKHC/graph.json","events_json":"https://pith.science/api/pith-number/H632NTESPKFTV7KG526LTTKKHC/events.json","paper":"https://pith.science/paper/H632NTES"},"agent_actions":{"view_html":"https://pith.science/pith/H632NTESPKFTV7KG526LTTKKHC","download_json":"https://pith.science/pith/H632NTESPKFTV7KG526LTTKKHC.json","view_paper":"https://pith.science/paper/H632NTES","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.7026&json=true","fetch_graph":"https://pith.science/api/pith-number/H632NTESPKFTV7KG526LTTKKHC/graph.json","fetch_events":"https://pith.science/api/pith-number/H632NTESPKFTV7KG526LTTKKHC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H632NTESPKFTV7KG526LTTKKHC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H632NTESPKFTV7KG526LTTKKHC/action/storage_attestation","attest_author":"https://pith.science/pith/H632NTESPKFTV7KG526LTTKKHC/action/author_attestation","sign_citation":"https://pith.science/pith/H632NTESPKFTV7KG526LTTKKHC/action/citation_signature","submit_replication":"https://pith.science/pith/H632NTESPKFTV7KG526LTTKKHC/action/replication_record"}},"created_at":"2026-05-18T01:23:16.864657+00:00","updated_at":"2026-05-18T01:23:16.864657+00:00"}