{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RUCZYADWXGFUY4SDZMCF7UDMA6","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":"21000d46cdd2aefc2c9eb1f0a2a79199b5d2d65ad2417df95c15def97ca85e9d","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-17T12:07:51Z","title_canon_sha256":"cbfdfb18d8302c61d0ad0c79817d01399031482fd720948edbe392ffecf23723"},"schema_version":"1.0","source":{"id":"1601.04280","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04280","created_at":"2026-05-18T01:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04280v1","created_at":"2026-05-18T01:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04280","created_at":"2026-05-18T01:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"RUCZYADWXGFU","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RUCZYADWXGFUY4SD","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RUCZYADW","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:f96520c017afa378d8538f80099772f4cdd40be8a45ced89a078a26ab89d0b14","target":"graph","created_at":"2026-05-18T01:22:45Z","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":"A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation error of the algorithm is analyzed and a theoretical error bound is presented. Finally, numerical examples illustrate that for a similar approximation error, the sparse LU algorithm is faster than recent state-of-the-art methods. The algorithm is completely parallelizable that enables to run on a GPU. The performance is tested on a GPU card, showing a signif","authors_text":"Amir Averbuch, Gil Shabat, Yariv Aizenbud","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-17T12:07:51Z","title":"Randomized LU Decomposition Using Sparse Projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04280","kind":"arxiv","version":1},"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:fda3bbda845a3a4743c356de05a6348f8c8d86881fa4f2ae914b616ac231c53a","target":"record","created_at":"2026-05-18T01:22:45Z","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":"21000d46cdd2aefc2c9eb1f0a2a79199b5d2d65ad2417df95c15def97ca85e9d","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-17T12:07:51Z","title_canon_sha256":"cbfdfb18d8302c61d0ad0c79817d01399031482fd720948edbe392ffecf23723"},"schema_version":"1.0","source":{"id":"1601.04280","kind":"arxiv","version":1}},"canonical_sha256":"8d059c0076b98b4c7243cb045fd06c07bcc890477802eead5e24dc8f41da553e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d059c0076b98b4c7243cb045fd06c07bcc890477802eead5e24dc8f41da553e","first_computed_at":"2026-05-18T01:22:45.439425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:45.439425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zNlwh7nnwmkd8+qQm8GjUTzX6aoaT39/uG5VwtAkpiHObniSW1b3odyhMl4Vpr0P8MBAPf4mYGovRTtGGB8tCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:45.439999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04280","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fda3bbda845a3a4743c356de05a6348f8c8d86881fa4f2ae914b616ac231c53a","sha256:f96520c017afa378d8538f80099772f4cdd40be8a45ced89a078a26ab89d0b14"],"state_sha256":"e57b87a36c2359477777971ea0326520a7cf14cb190b1dbec30e6e688fe419c2"}