{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:L3M23HGBCQT6ZTIUN3C5JO6Y7K","short_pith_number":"pith:L3M23HGB","canonical_record":{"source":{"id":"1401.0417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-01-02T11:19:11Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"2da2a849c0ce61e8c3e1b9cbb8e4195b8cdadcdb0fd4dcea27dd73f69770decb","abstract_canon_sha256":"8bff0737ef0ee8792f5e9c7522dabf93433c12afb10aa5770c0bebd9739cb5c4"},"schema_version":"1.0"},"canonical_sha256":"5ed9ad9cc11427eccd146ec5d4bbd8faa31f2af05ff7e076d5ac79e9ba219bfc","source":{"kind":"arxiv","id":"1401.0417","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0417","created_at":"2026-05-18T02:50:58Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0417v2","created_at":"2026-05-18T02:50:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0417","created_at":"2026-05-18T02:50:58Z"},{"alias_kind":"pith_short_12","alias_value":"L3M23HGBCQT6","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L3M23HGBCQT6ZTIU","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L3M23HGB","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:L3M23HGBCQT6ZTIUN3C5JO6Y7K","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-01-02T11:19:11Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"2da2a849c0ce61e8c3e1b9cbb8e4195b8cdadcdb0fd4dcea27dd73f69770decb","abstract_canon_sha256":"8bff0737ef0ee8792f5e9c7522dabf93433c12afb10aa5770c0bebd9739cb5c4"},"schema_version":"1.0"},"canonical_sha256":"5ed9ad9cc11427eccd146ec5d4bbd8faa31f2af05ff7e076d5ac79e9ba219bfc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:58.631375Z","signature_b64":"IXN6YgjGIS0g0yGkaMsZ5tYEMImkVaVLP2FoCK3tow7uO0MXCk8zdFFhf5MxkzicyvWnPQp+0RlsRl/8/EAYCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ed9ad9cc11427eccd146ec5d4bbd8faa31f2af05ff7e076d5ac79e9ba219bfc","last_reissued_at":"2026-05-18T02:50:58.630734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:58.630734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0417","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hcAI0vWoOidi5uynm6TqKQGyYCpRDHfvzGq5+mAUOXIsntO0hrH5yeyij1z/VxlL8g+lWlh/mLf+V9RsZGFkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:42:10.480247Z"},"content_sha256":"9290594ff6a9762bb25526a011895787f90abd4ced5934b3fd3bec92ab4c51bb","schema_version":"1.0","event_id":"sha256:9290594ff6a9762bb25526a011895787f90abd4ced5934b3fd3bec92ab4c51bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:L3M23HGBCQT6ZTIUN3C5JO6Y7K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faster SVD-Truncated Least-Squares Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.DS","authors_text":"Christos Boutsidis, Malik Magdon-Ismail","submitted_at":"2014-01-02T11:19:11Z","abstract_excerpt":"We develop a fast algorithm for computing the \"SVD-truncated\" regularized solution to the least-squares problem: $ \\min_{\\x} \\TNorm{\\matA \\x - \\b}. $ Let $\\matA_k$ of rank $k$ be the best rank $k$ matrix computed via the SVD of $\\matA$. Then, the SVD-truncated regularized solution is: $ \\x_k = \\pinv{\\matA}_k \\b. $ If $\\matA$ is $m \\times n$, then, it takes $O(m n \\min\\{m,n\\})$ time to compute $\\x_k $ using the SVD of \\math{\\matA}. We give an approximation algorithm for \\math{\\x_k} which constructs a rank-\\math{k} approximation $\\tilde{\\matA}_{k}$ and computes $ \\tilde{\\x}_{k} = \\pinv{\\tilde\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0417","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkgTZLkh5RtJKYIDeB6paMR8ftY3GnVc/Hyyqf+TA3kGSvUsy5SAmtV1TeVrDOC72xjGC8a/v4PMABEop5vkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:42:10.480777Z"},"content_sha256":"d84d1378008877af4cb0f5f86a6bc6a400c9d074be22adeacc9f7ba2a0e0e495","schema_version":"1.0","event_id":"sha256:d84d1378008877af4cb0f5f86a6bc6a400c9d074be22adeacc9f7ba2a0e0e495"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L3M23HGBCQT6ZTIUN3C5JO6Y7K/bundle.json","state_url":"https://pith.science/pith/L3M23HGBCQT6ZTIUN3C5JO6Y7K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L3M23HGBCQT6ZTIUN3C5JO6Y7K/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T18:42:10Z","links":{"resolver":"https://pith.science/pith/L3M23HGBCQT6ZTIUN3C5JO6Y7K","bundle":"https://pith.science/pith/L3M23HGBCQT6ZTIUN3C5JO6Y7K/bundle.json","state":"https://pith.science/pith/L3M23HGBCQT6ZTIUN3C5JO6Y7K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L3M23HGBCQT6ZTIUN3C5JO6Y7K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L3M23HGBCQT6ZTIUN3C5JO6Y7K","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":"8bff0737ef0ee8792f5e9c7522dabf93433c12afb10aa5770c0bebd9739cb5c4","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-01-02T11:19:11Z","title_canon_sha256":"2da2a849c0ce61e8c3e1b9cbb8e4195b8cdadcdb0fd4dcea27dd73f69770decb"},"schema_version":"1.0","source":{"id":"1401.0417","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0417","created_at":"2026-05-18T02:50:58Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0417v2","created_at":"2026-05-18T02:50:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0417","created_at":"2026-05-18T02:50:58Z"},{"alias_kind":"pith_short_12","alias_value":"L3M23HGBCQT6","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L3M23HGBCQT6ZTIU","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L3M23HGB","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:d84d1378008877af4cb0f5f86a6bc6a400c9d074be22adeacc9f7ba2a0e0e495","target":"graph","created_at":"2026-05-18T02:50:58Z","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 develop a fast algorithm for computing the \"SVD-truncated\" regularized solution to the least-squares problem: $ \\min_{\\x} \\TNorm{\\matA \\x - \\b}. $ Let $\\matA_k$ of rank $k$ be the best rank $k$ matrix computed via the SVD of $\\matA$. Then, the SVD-truncated regularized solution is: $ \\x_k = \\pinv{\\matA}_k \\b. $ If $\\matA$ is $m \\times n$, then, it takes $O(m n \\min\\{m,n\\})$ time to compute $\\x_k $ using the SVD of \\math{\\matA}. We give an approximation algorithm for \\math{\\x_k} which constructs a rank-\\math{k} approximation $\\tilde{\\matA}_{k}$ and computes $ \\tilde{\\x}_{k} = \\pinv{\\tilde\\ma","authors_text":"Christos Boutsidis, Malik Magdon-Ismail","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-01-02T11:19:11Z","title":"Faster SVD-Truncated Least-Squares Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0417","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":"sha256:9290594ff6a9762bb25526a011895787f90abd4ced5934b3fd3bec92ab4c51bb","target":"record","created_at":"2026-05-18T02:50:58Z","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":"8bff0737ef0ee8792f5e9c7522dabf93433c12afb10aa5770c0bebd9739cb5c4","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-01-02T11:19:11Z","title_canon_sha256":"2da2a849c0ce61e8c3e1b9cbb8e4195b8cdadcdb0fd4dcea27dd73f69770decb"},"schema_version":"1.0","source":{"id":"1401.0417","kind":"arxiv","version":2}},"canonical_sha256":"5ed9ad9cc11427eccd146ec5d4bbd8faa31f2af05ff7e076d5ac79e9ba219bfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ed9ad9cc11427eccd146ec5d4bbd8faa31f2af05ff7e076d5ac79e9ba219bfc","first_computed_at":"2026-05-18T02:50:58.630734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:58.630734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IXN6YgjGIS0g0yGkaMsZ5tYEMImkVaVLP2FoCK3tow7uO0MXCk8zdFFhf5MxkzicyvWnPQp+0RlsRl/8/EAYCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:58.631375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0417","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9290594ff6a9762bb25526a011895787f90abd4ced5934b3fd3bec92ab4c51bb","sha256:d84d1378008877af4cb0f5f86a6bc6a400c9d074be22adeacc9f7ba2a0e0e495"],"state_sha256":"f5663326893605f4bb10e6e208f8cf52e905746285611a23f9cad9774e3d1109"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zg12vBZRrsRCQ825zas+mV23CGoDAPahqTQVCS4bcymywwCT6inzgA9CjG5wbCUfAtAvRKZjcUn/0QDgbAfBAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:42:10.484069Z","bundle_sha256":"244ffc191e42d4d92c5c18a090b54788fe264972713e56353d79d0cea7dd76ba"}}