{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:M2UNT6BW2DANBFKVK3TU4V4ANW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0584b7c88d8ee3ec551d7a2e403c62afd0e04cd56119d5fc416f17c4e4a939f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-20T14:37:49Z","title_canon_sha256":"46ae1988a33dcf71b4c02a12f7c16750ee40d9102aa717149a5dbd7d6438fe3c"},"schema_version":"1.0","source":{"id":"1402.5011","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5011","created_at":"2026-05-18T02:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5011v2","created_at":"2026-05-18T02:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5011","created_at":"2026-05-18T02:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"M2UNT6BW2DAN","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M2UNT6BW2DANBFKV","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M2UNT6BW","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:9fdd8356b27d9510832c63edabe588a83c24ea49443df1531a2dc867186dfd21","target":"graph","created_at":"2026-05-18T02:32:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms. We prove that for certain parameters (smoothness and norm of the $r$th derivative) this problem is intractable while for other parameters the problem is tractable and the complexity is only polynomial in the dimension for every fixed $\\varepsilon>0$. For randomized algorithms we completely characterize the set of parameters that lead to easy or difficult problems, respectively. In the \"difficult\" case we modify the class to obtain a tractable prob","authors_text":"Daniel Rudolf, Erich Novak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-20T14:37:49Z","title":"Tractability of the approximation of high-dimensional rank one tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5011","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9410a40c4456d7241bcff3f0ef6d376d3c8e34c11642f5769fba20f3ee03b79b","target":"record","created_at":"2026-05-18T02:32:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0584b7c88d8ee3ec551d7a2e403c62afd0e04cd56119d5fc416f17c4e4a939f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-20T14:37:49Z","title_canon_sha256":"46ae1988a33dcf71b4c02a12f7c16750ee40d9102aa717149a5dbd7d6438fe3c"},"schema_version":"1.0","source":{"id":"1402.5011","kind":"arxiv","version":2}},"canonical_sha256":"66a8d9f836d0c0d0955556e74e57806db4ac4ab2f75255831d491084bc83ac6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66a8d9f836d0c0d0955556e74e57806db4ac4ab2f75255831d491084bc83ac6e","first_computed_at":"2026-05-18T02:32:22.376269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:22.376269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q6nqEUVYfnf8MP41vRN23C0xpw7/2u6s4YD4bWLQn/jj/1ld0a7V61hvt+ynNDQIXbs/ITLZiPeA/kW5CYLNBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:22.376677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5011","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9410a40c4456d7241bcff3f0ef6d376d3c8e34c11642f5769fba20f3ee03b79b","sha256:9fdd8356b27d9510832c63edabe588a83c24ea49443df1531a2dc867186dfd21"],"state_sha256":"2a2c454768a44e8f321f15241506b20ad6f85196ddfb540d64fdb13c227d06c7"}