{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Y2LR2QATGNYND2JZLCZOML3JR7","short_pith_number":"pith:Y2LR2QAT","canonical_record":{"source":{"id":"1512.09156","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-30T21:29:57Z","cross_cats_sorted":["cs.LG","cs.NA","math.IT"],"title_canon_sha256":"701d95094c0195374d7607952896e9b775f2d8bb9b9fea4daad590a36147fd0c","abstract_canon_sha256":"982ef816c3ccd192066c68ec77168b147290c845e6ccf91406ae998883ff04ef"},"schema_version":"1.0"},"canonical_sha256":"c6971d40133370d1e93958b2e62f698feb3ca6a13f22cfdfffae52299faac185","source":{"kind":"arxiv","id":"1512.09156","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09156","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09156v3","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09156","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"pith_short_12","alias_value":"Y2LR2QATGNYN","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"Y2LR2QATGNYND2JZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"Y2LR2QAT","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Y2LR2QATGNYND2JZLCZOML3JR7","target":"record","payload":{"canonical_record":{"source":{"id":"1512.09156","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-30T21:29:57Z","cross_cats_sorted":["cs.LG","cs.NA","math.IT"],"title_canon_sha256":"701d95094c0195374d7607952896e9b775f2d8bb9b9fea4daad590a36147fd0c","abstract_canon_sha256":"982ef816c3ccd192066c68ec77168b147290c845e6ccf91406ae998883ff04ef"},"schema_version":"1.0"},"canonical_sha256":"c6971d40133370d1e93958b2e62f698feb3ca6a13f22cfdfffae52299faac185","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:12.709511Z","signature_b64":"tltb3dUByHGR9wZDA1baC20HIQ9jEzaPNImGjQOFagkWk4WxNWYbcmbslm2r3xBxduJYKiWiKhYVCwvH9gbECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6971d40133370d1e93958b2e62f698feb3ca6a13f22cfdfffae52299faac185","last_reissued_at":"2026-05-18T00:06:12.708912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:12.708912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.09156","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JMk2D/ptG19H/iYQDJbl0kTf9z4Xpelm1vcbk//yzqjURMxKm68DXmPDwZt8pfCrnK8umUF5H8SEXiPUO0ArCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:42:25.629143Z"},"content_sha256":"c98e44e4f4f9543f3c9038eaae08274ceb5658d307dc65c2981990c7dd421ccd","schema_version":"1.0","event_id":"sha256:c98e44e4f4f9543f3c9038eaae08274ceb5658d307dc65c2981990c7dd421ccd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Y2LR2QATGNYND2JZLCZOML3JR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low rank approximation and decomposition of large matrices using error correcting codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.IT"],"primary_cat":"cs.IT","authors_text":"Arya Mazumdar, Shashanka Ubaru, Yousef Saad","submitted_at":"2015-12-30T21:29:57Z","abstract_excerpt":"Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate singular value decompositions of large matrices. Similar ideas were used to solve least squares regression problems. In this paper, we show how matrices from error correcting codes can be used to find such low rank approximations and matrix decompositions, and extend the framework to linear least squares regression problems. The benefits of using these code"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09156","kind":"arxiv","version":3},"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":"2026-05-18T00:06:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3PEjqYG2PkjU+tVOV7/mZtZq+UgAdXAqQkEeejtAnEcABdcQfPRWp5oWJDfxv2v1tWeMyTlT19STQohefCZjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:42:25.629528Z"},"content_sha256":"3ff19c2a37edb0fb8893b0ef88edbb4babbfac190e3203f5236c5e19238139f1","schema_version":"1.0","event_id":"sha256:3ff19c2a37edb0fb8893b0ef88edbb4babbfac190e3203f5236c5e19238139f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2LR2QATGNYND2JZLCZOML3JR7/bundle.json","state_url":"https://pith.science/pith/Y2LR2QATGNYND2JZLCZOML3JR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2LR2QATGNYND2JZLCZOML3JR7/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":"2026-05-26T03:42:25Z","links":{"resolver":"https://pith.science/pith/Y2LR2QATGNYND2JZLCZOML3JR7","bundle":"https://pith.science/pith/Y2LR2QATGNYND2JZLCZOML3JR7/bundle.json","state":"https://pith.science/pith/Y2LR2QATGNYND2JZLCZOML3JR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2LR2QATGNYND2JZLCZOML3JR7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Y2LR2QATGNYND2JZLCZOML3JR7","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":"982ef816c3ccd192066c68ec77168b147290c845e6ccf91406ae998883ff04ef","cross_cats_sorted":["cs.LG","cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-30T21:29:57Z","title_canon_sha256":"701d95094c0195374d7607952896e9b775f2d8bb9b9fea4daad590a36147fd0c"},"schema_version":"1.0","source":{"id":"1512.09156","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09156","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09156v3","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09156","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"pith_short_12","alias_value":"Y2LR2QATGNYN","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"Y2LR2QATGNYND2JZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"Y2LR2QAT","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:3ff19c2a37edb0fb8893b0ef88edbb4babbfac190e3203f5236c5e19238139f1","target":"graph","created_at":"2026-05-18T00:06:12Z","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":"Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate singular value decompositions of large matrices. Similar ideas were used to solve least squares regression problems. In this paper, we show how matrices from error correcting codes can be used to find such low rank approximations and matrix decompositions, and extend the framework to linear least squares regression problems. The benefits of using these code","authors_text":"Arya Mazumdar, Shashanka Ubaru, Yousef Saad","cross_cats":["cs.LG","cs.NA","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-30T21:29:57Z","title":"Low rank approximation and decomposition of large matrices using error correcting codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09156","kind":"arxiv","version":3},"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:c98e44e4f4f9543f3c9038eaae08274ceb5658d307dc65c2981990c7dd421ccd","target":"record","created_at":"2026-05-18T00:06:12Z","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":"982ef816c3ccd192066c68ec77168b147290c845e6ccf91406ae998883ff04ef","cross_cats_sorted":["cs.LG","cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-30T21:29:57Z","title_canon_sha256":"701d95094c0195374d7607952896e9b775f2d8bb9b9fea4daad590a36147fd0c"},"schema_version":"1.0","source":{"id":"1512.09156","kind":"arxiv","version":3}},"canonical_sha256":"c6971d40133370d1e93958b2e62f698feb3ca6a13f22cfdfffae52299faac185","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6971d40133370d1e93958b2e62f698feb3ca6a13f22cfdfffae52299faac185","first_computed_at":"2026-05-18T00:06:12.708912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:12.708912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tltb3dUByHGR9wZDA1baC20HIQ9jEzaPNImGjQOFagkWk4WxNWYbcmbslm2r3xBxduJYKiWiKhYVCwvH9gbECQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:12.709511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.09156","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c98e44e4f4f9543f3c9038eaae08274ceb5658d307dc65c2981990c7dd421ccd","sha256:3ff19c2a37edb0fb8893b0ef88edbb4babbfac190e3203f5236c5e19238139f1"],"state_sha256":"41c39a8fd8946a0f954f0a6ec4023de0ac154bc636560c63aac6fbf7f70fa708"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2Ast+/oHhyGr4fFozG4DSoD50TLmr5s+cfmb2qffrKoS0fX6HTYs/zsIsY1I+xqLGvzr94odGxscXhWbiBLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:42:25.633255Z","bundle_sha256":"717e0c9244b2e332b401e5cf102d11cfef49a6af7d166a79a121bea1a96cbc95"}}