{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZBEIU33RZA6AWETL4NQUMRTAGI","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":"257691938e1929b05a1fd295f79074faa75f532b4c7501e5f1dd9eb63b48673d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-24T19:56:08Z","title_canon_sha256":"0cdfe5ab29889ca22c28d5cf61b821dce242c844717bc920425afaf4075db60f"},"schema_version":"1.0","source":{"id":"1503.07157","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07157","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07157v2","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07157","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"pith_short_12","alias_value":"ZBEIU33RZA6A","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZBEIU33RZA6AWETL","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZBEIU33R","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:3991c4ae9690a7e330b1ee25857ba35421ceee17ead8003461864aae662638d3","target":"graph","created_at":"2026-05-18T01:44:11Z","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":"This manuscript describes a technique for computing partial rank-revealing factorizations, such as, e.g, a partial QR factorization or a partial singular value decomposition. The method takes as input a tolerance $\\varepsilon$ and an $m\\times n$ matrix $A$, and returns an approximate low rank factorization of $A$ that is accurate to within precision $\\varepsilon$ in the Frobenius norm (or some other easily computed norm). The rank $k$ of the computed factorization (which is an output of the algorithm) is in all examples we examined very close to the theoretically optimal $\\varepsilon$-rank. Th","authors_text":"Per-Gunnar Martinsson, Sergey Voronin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-24T19:56:08Z","title":"A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07157","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":"sha256:7739f9c843c169afa8c57b48eec05515ceb21929f47d3d2378a3f312af004262","target":"record","created_at":"2026-05-18T01:44:11Z","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":"257691938e1929b05a1fd295f79074faa75f532b4c7501e5f1dd9eb63b48673d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-24T19:56:08Z","title_canon_sha256":"0cdfe5ab29889ca22c28d5cf61b821dce242c844717bc920425afaf4075db60f"},"schema_version":"1.0","source":{"id":"1503.07157","kind":"arxiv","version":2}},"canonical_sha256":"c8488a6f71c83c0b126be361464660320cbe9c6477c0ee815e9d8f8de4a60280","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8488a6f71c83c0b126be361464660320cbe9c6477c0ee815e9d8f8de4a60280","first_computed_at":"2026-05-18T01:44:11.167455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:11.167455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VoZdNaTlrIZ6RruKWVG+nvDXDWx09z5/9I+LN1M8FB9dYgnR9DZ+IvN6V3omSRz1p4Vbe77oT9Ne6NyjVY7cAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:11.168079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07157","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7739f9c843c169afa8c57b48eec05515ceb21929f47d3d2378a3f312af004262","sha256:3991c4ae9690a7e330b1ee25857ba35421ceee17ead8003461864aae662638d3"],"state_sha256":"7260a65cbf0d7d7cb842c9e55fb692549a7a8a7116fae2b26ad4e50532311ec9"}