{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OHCMEHVGW5QQOUOKYPALT5YNLC","short_pith_number":"pith:OHCMEHVG","canonical_record":{"source":{"id":"1606.09402","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-30T09:14:53Z","cross_cats_sorted":["cs.DC","cs.DS","cs.NA"],"title_canon_sha256":"cd68cdb8f300e33c29a54d4d9ca6515e4cf69f4b6bfb8e76c77c842bd0d7c0bd","abstract_canon_sha256":"80155608b407f825f1e227370b73b6c78f089c3093065daf6e70c4f1617f0d6f"},"schema_version":"1.0"},"canonical_sha256":"71c4c21ea6b7610751cac3c0b9f70d589fc4bc8099d4d7f531b620fe5ee2f779","source":{"kind":"arxiv","id":"1606.09402","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.09402","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1606.09402v3","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.09402","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"OHCMEHVGW5QQ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OHCMEHVGW5QQOUOK","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OHCMEHVG","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OHCMEHVGW5QQOUOKYPALT5YNLC","target":"record","payload":{"canonical_record":{"source":{"id":"1606.09402","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-30T09:14:53Z","cross_cats_sorted":["cs.DC","cs.DS","cs.NA"],"title_canon_sha256":"cd68cdb8f300e33c29a54d4d9ca6515e4cf69f4b6bfb8e76c77c842bd0d7c0bd","abstract_canon_sha256":"80155608b407f825f1e227370b73b6c78f089c3093065daf6e70c4f1617f0d6f"},"schema_version":"1.0"},"canonical_sha256":"71c4c21ea6b7610751cac3c0b9f70d589fc4bc8099d4d7f531b620fe5ee2f779","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:57.129740Z","signature_b64":"8XBKsq7qc8MH8sNvKYvL2g6NOTU8B53PwpJaJnFDTX5SjF0mR2LYBvUQovxgBTIK5anvqXBblsal+rJl2ctoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71c4c21ea6b7610751cac3c0b9f70d589fc4bc8099d4d7f531b620fe5ee2f779","last_reissued_at":"2026-05-18T00:23:57.129201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:57.129201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.09402","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":"2026-05-18T00:23:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3cBpjFQyXEogtCpXjDHz9jeY8Ya43rj1Rf4Mo1et23YqOKX3ior1jPYxSM/OhjyC31bPSqAK8Ff01omk0x3BBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:29:13.037654Z"},"content_sha256":"c69b5f6fcc575a0b8b15598b6a1ab869e8b4376f34ec45c89da4b19fb9ac6761","schema_version":"1.0","event_id":"sha256:c69b5f6fcc575a0b8b15598b6a1ab869e8b4376f34ec45c89da4b19fb9ac6761"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OHCMEHVGW5QQOUOKYPALT5YNLC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Randomized Algorithms for the Fixed-Precision Low-Rank Matrix Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.DS","cs.NA"],"primary_cat":"math.NA","authors_text":"Wenjian Yu, Yaohang Li, Yu Gu","submitted_at":"2016-06-30T09:14:53Z","abstract_excerpt":"Randomized algorithms for low-rank matrix approximation are investigated, with the emphasis on the fixed-precision problem and computational efficiency for handling large matrices. The algorithms are based on the so-called QB factorization, where Q is an orthonormal matrix. Firstly, a mechanism for calculating the approximation error in Frobenius norm is proposed, which enables efficient adaptive rank determination for large and/or sparse matrix. It can be combined with any QB-form factorization algorithm in which B's rows are incrementally generated. Based on the blocked randQB algorithm by P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09402","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":"2026-05-18T00:23:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RIFCgIThFcUvwoUqLJWC9yNRW9CbALVbsCDs+UlUfWd/LfjGe07D7Aifqqt85sKiKBZ1QG+QiZiuIAtiOjZFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:29:13.038031Z"},"content_sha256":"44f89d2a539ffc49ebb65578d34d9924de3abef272b51e8fe47ecfc869e85ecf","schema_version":"1.0","event_id":"sha256:44f89d2a539ffc49ebb65578d34d9924de3abef272b51e8fe47ecfc869e85ecf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OHCMEHVGW5QQOUOKYPALT5YNLC/bundle.json","state_url":"https://pith.science/pith/OHCMEHVGW5QQOUOKYPALT5YNLC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OHCMEHVGW5QQOUOKYPALT5YNLC/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":"2026-06-01T14:29:13Z","links":{"resolver":"https://pith.science/pith/OHCMEHVGW5QQOUOKYPALT5YNLC","bundle":"https://pith.science/pith/OHCMEHVGW5QQOUOKYPALT5YNLC/bundle.json","state":"https://pith.science/pith/OHCMEHVGW5QQOUOKYPALT5YNLC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OHCMEHVGW5QQOUOKYPALT5YNLC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OHCMEHVGW5QQOUOKYPALT5YNLC","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":"80155608b407f825f1e227370b73b6c78f089c3093065daf6e70c4f1617f0d6f","cross_cats_sorted":["cs.DC","cs.DS","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-30T09:14:53Z","title_canon_sha256":"cd68cdb8f300e33c29a54d4d9ca6515e4cf69f4b6bfb8e76c77c842bd0d7c0bd"},"schema_version":"1.0","source":{"id":"1606.09402","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.09402","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1606.09402v3","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.09402","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"OHCMEHVGW5QQ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OHCMEHVGW5QQOUOK","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OHCMEHVG","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:44f89d2a539ffc49ebb65578d34d9924de3abef272b51e8fe47ecfc869e85ecf","target":"graph","created_at":"2026-05-18T00:23:57Z","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":"Randomized algorithms for low-rank matrix approximation are investigated, with the emphasis on the fixed-precision problem and computational efficiency for handling large matrices. The algorithms are based on the so-called QB factorization, where Q is an orthonormal matrix. Firstly, a mechanism for calculating the approximation error in Frobenius norm is proposed, which enables efficient adaptive rank determination for large and/or sparse matrix. It can be combined with any QB-form factorization algorithm in which B's rows are incrementally generated. Based on the blocked randQB algorithm by P","authors_text":"Wenjian Yu, Yaohang Li, Yu Gu","cross_cats":["cs.DC","cs.DS","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-30T09:14:53Z","title":"Efficient Randomized Algorithms for the Fixed-Precision Low-Rank Matrix Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09402","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:c69b5f6fcc575a0b8b15598b6a1ab869e8b4376f34ec45c89da4b19fb9ac6761","target":"record","created_at":"2026-05-18T00:23:57Z","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":"80155608b407f825f1e227370b73b6c78f089c3093065daf6e70c4f1617f0d6f","cross_cats_sorted":["cs.DC","cs.DS","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-30T09:14:53Z","title_canon_sha256":"cd68cdb8f300e33c29a54d4d9ca6515e4cf69f4b6bfb8e76c77c842bd0d7c0bd"},"schema_version":"1.0","source":{"id":"1606.09402","kind":"arxiv","version":3}},"canonical_sha256":"71c4c21ea6b7610751cac3c0b9f70d589fc4bc8099d4d7f531b620fe5ee2f779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71c4c21ea6b7610751cac3c0b9f70d589fc4bc8099d4d7f531b620fe5ee2f779","first_computed_at":"2026-05-18T00:23:57.129201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:57.129201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8XBKsq7qc8MH8sNvKYvL2g6NOTU8B53PwpJaJnFDTX5SjF0mR2LYBvUQovxgBTIK5anvqXBblsal+rJl2ctoAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:57.129740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.09402","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c69b5f6fcc575a0b8b15598b6a1ab869e8b4376f34ec45c89da4b19fb9ac6761","sha256:44f89d2a539ffc49ebb65578d34d9924de3abef272b51e8fe47ecfc869e85ecf"],"state_sha256":"def5458d656ecd5fd5e3a07f786562f69c492006f3c27507c732745dc0498eaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p8mOlwtklWwTi5PM62P4+x6wxSyQFWR7BGtaKhvp8NT1tZJX4cVdnXbob8+rf5QaL4Ne1IVzfvt2Bj2Qv0ZaAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:29:13.040071Z","bundle_sha256":"938ceda0abb7d2168a4bb29e2124393f2555bb6e3fe3adfb9876ba29046c84ce"}}