{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:PT7UNO4TAUIUSUWSNES3IRG2GY","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":"f06255613653955aa262b028da4132b95263c120a7df1064821e5a22bbd9c93f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-07-12T18:23:28Z","title_canon_sha256":"a5a4b9cb1bdbf969d517a66f07dfec72ea43996633ac2055ece0197896c28c4a"},"schema_version":"1.0","source":{"id":"2107.05672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.05672","created_at":"2026-07-05T02:57:26Z"},{"alias_kind":"arxiv_version","alias_value":"2107.05672v1","created_at":"2026-07-05T02:57:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.05672","created_at":"2026-07-05T02:57:26Z"},{"alias_kind":"pith_short_12","alias_value":"PT7UNO4TAUIU","created_at":"2026-07-05T02:57:26Z"},{"alias_kind":"pith_short_16","alias_value":"PT7UNO4TAUIUSUWS","created_at":"2026-07-05T02:57:26Z"},{"alias_kind":"pith_short_8","alias_value":"PT7UNO4T","created_at":"2026-07-05T02:57:26Z"}],"graph_snapshots":[{"event_id":"sha256:c72d736b4f28f5ace1e8840ff9797ce4fc44fa81df554df56dc1bb261b0f1aaf","target":"graph","created_at":"2026-07-05T02:57:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2107.05672/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Sketching is a powerful dimensionality reduction technique for accelerating algorithms for data analysis. A crucial step in sketching methods is to compute a subspace embedding (SE) for a large matrix $\\mathbf{A} \\in \\mathbb{R}^{N \\times d}$. SE's are the primary tool for obtaining extremely efficient solutions for many linear-algebraic tasks, such as least squares regression and low rank approximation. Computing an SE often requires an explicit representation of $\\mathbf{A}$ and running time proportional to the size of $\\mathbf{A}$. However, if $\\mathbf{A}= \\mathbf{T}_1 \\Join \\mathbf{T}_2 \\Jo","authors_text":"Alireza Samadian, David P. Woodruff, Peng Ye, Rajesh Jayaram","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-07-12T18:23:28Z","title":"In-Database Regression in Input Sparsity Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.05672","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:f6ebdba538ec00b2ae7b47f294327d943f92188a7224fecf21572d11c7650aba","target":"record","created_at":"2026-07-05T02:57:26Z","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":"f06255613653955aa262b028da4132b95263c120a7df1064821e5a22bbd9c93f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-07-12T18:23:28Z","title_canon_sha256":"a5a4b9cb1bdbf969d517a66f07dfec72ea43996633ac2055ece0197896c28c4a"},"schema_version":"1.0","source":{"id":"2107.05672","kind":"arxiv","version":1}},"canonical_sha256":"7cff46bb9305114952d26925b444da36383566d96a16a528abd2d1e9737dabc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cff46bb9305114952d26925b444da36383566d96a16a528abd2d1e9737dabc0","first_computed_at":"2026-07-05T02:57:26.759175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:57:26.759175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SG4icGWrjPCZLXgApHp3FR7HAFDQcEomaG5OWMJ04qBcMqzEDrwnCHz2X0BdSd+zSDZohfTQrX8eJF9XtB1vAw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:57:26.759625Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.05672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6ebdba538ec00b2ae7b47f294327d943f92188a7224fecf21572d11c7650aba","sha256:c72d736b4f28f5ace1e8840ff9797ce4fc44fa81df554df56dc1bb261b0f1aaf"],"state_sha256":"08cf806f657ac49aca398c9afc68b996ab16416de61e54f60ac56e1e41ad535e"}