{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JKN7JRUPPMT3WLKVARANGJYWN7","short_pith_number":"pith:JKN7JRUP","canonical_record":{"source":{"id":"1609.02258","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NA","submitted_at":"2016-09-08T04:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"2d49059b1f26da3ccd5ff8c14e295477377421553b44666d2128cb65a31741c3","abstract_canon_sha256":"f0dbba67f7419e6d3f784cfab0d3c7f5c72441c2cb51df8c1953944a179df083"},"schema_version":"1.0"},"canonical_sha256":"4a9bf4c68f7b27bb2d550440d327166fe5a0310a9222a59efc3988f3265d0cb5","source":{"kind":"arxiv","id":"1609.02258","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02258","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02258v1","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02258","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"JKN7JRUPPMT3","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JKN7JRUPPMT3WLKV","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JKN7JRUP","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JKN7JRUPPMT3WLKVARANGJYWN7","target":"record","payload":{"canonical_record":{"source":{"id":"1609.02258","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NA","submitted_at":"2016-09-08T04:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"2d49059b1f26da3ccd5ff8c14e295477377421553b44666d2128cb65a31741c3","abstract_canon_sha256":"f0dbba67f7419e6d3f784cfab0d3c7f5c72441c2cb51df8c1953944a179df083"},"schema_version":"1.0"},"canonical_sha256":"4a9bf4c68f7b27bb2d550440d327166fe5a0310a9222a59efc3988f3265d0cb5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:55.094603Z","signature_b64":"4pciJOK4JheGvkg5Q7HbMwy1jtqivQkkxetRMH7QAOZo4DCzKYEHYdz5qwRMfT5vUxrzVW648/ILqzbam/aODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a9bf4c68f7b27bb2d550440d327166fe5a0310a9222a59efc3988f3265d0cb5","last_reissued_at":"2026-05-18T01:04:55.093990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:55.093990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.02258","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HOa7kjT0TQCKr6WbYYzdT69iV/QXv39DZt3p7Ol6Lb9/xMD6L1nlF5kBJ8pU1Lwc9C3yhcxpnOhy/A9108frCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:55:56.656447Z"},"content_sha256":"e21debeb2b6cf47ea06287a118f83a83659355a9280f8b79b2cc9fa5a4d67fc7","schema_version":"1.0","event_id":"sha256:e21debeb2b6cf47ea06287a118f83a83659355a9280f8b79b2cc9fa5a4d67fc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JKN7JRUPPMT3WLKVARANGJYWN7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tighter bound of Sketched Generalized Matrix Approximation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"Haishan Ye, Qiaoming Ye, Zhihua Zhang","submitted_at":"2016-09-08T04:01:02Z","abstract_excerpt":"Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and larger dataset, more and more efficient generalized matrix approximation algorithems become a crucially important research issue. In this paper, we find new sketching techniques to reduce the size of the original data matrix to develop new matrix approximation algorithms. Our results derive a much tighter bound for the approximation than previous works: we obta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02258","kind":"arxiv","version":1},"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":"2026-05-18T01:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fffNaAfHNeOyW9zROaqSxtX+ZEWFUYiEGdwrdGTCcq4JUQQ8qSjNM7NNYYGEPvoujFHV9ltcqOB1KPmrL2D/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:55:56.657227Z"},"content_sha256":"84c93e543270f78eabcda523df94b140a3a41e3b4f947caf3354458561f3b08f","schema_version":"1.0","event_id":"sha256:84c93e543270f78eabcda523df94b140a3a41e3b4f947caf3354458561f3b08f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JKN7JRUPPMT3WLKVARANGJYWN7/bundle.json","state_url":"https://pith.science/pith/JKN7JRUPPMT3WLKVARANGJYWN7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JKN7JRUPPMT3WLKVARANGJYWN7/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":"2026-06-11T16:55:56Z","links":{"resolver":"https://pith.science/pith/JKN7JRUPPMT3WLKVARANGJYWN7","bundle":"https://pith.science/pith/JKN7JRUPPMT3WLKVARANGJYWN7/bundle.json","state":"https://pith.science/pith/JKN7JRUPPMT3WLKVARANGJYWN7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JKN7JRUPPMT3WLKVARANGJYWN7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JKN7JRUPPMT3WLKVARANGJYWN7","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":"f0dbba67f7419e6d3f784cfab0d3c7f5c72441c2cb51df8c1953944a179df083","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NA","submitted_at":"2016-09-08T04:01:02Z","title_canon_sha256":"2d49059b1f26da3ccd5ff8c14e295477377421553b44666d2128cb65a31741c3"},"schema_version":"1.0","source":{"id":"1609.02258","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02258","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02258v1","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02258","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"JKN7JRUPPMT3","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JKN7JRUPPMT3WLKV","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JKN7JRUP","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:84c93e543270f78eabcda523df94b140a3a41e3b4f947caf3354458561f3b08f","target":"graph","created_at":"2026-05-18T01:04:55Z","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":"Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and larger dataset, more and more efficient generalized matrix approximation algorithems become a crucially important research issue. In this paper, we find new sketching techniques to reduce the size of the original data matrix to develop new matrix approximation algorithms. Our results derive a much tighter bound for the approximation than previous works: we obta","authors_text":"Haishan Ye, Qiaoming Ye, Zhihua Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NA","submitted_at":"2016-09-08T04:01:02Z","title":"Tighter bound of Sketched Generalized Matrix Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02258","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:e21debeb2b6cf47ea06287a118f83a83659355a9280f8b79b2cc9fa5a4d67fc7","target":"record","created_at":"2026-05-18T01:04:55Z","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":"f0dbba67f7419e6d3f784cfab0d3c7f5c72441c2cb51df8c1953944a179df083","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NA","submitted_at":"2016-09-08T04:01:02Z","title_canon_sha256":"2d49059b1f26da3ccd5ff8c14e295477377421553b44666d2128cb65a31741c3"},"schema_version":"1.0","source":{"id":"1609.02258","kind":"arxiv","version":1}},"canonical_sha256":"4a9bf4c68f7b27bb2d550440d327166fe5a0310a9222a59efc3988f3265d0cb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a9bf4c68f7b27bb2d550440d327166fe5a0310a9222a59efc3988f3265d0cb5","first_computed_at":"2026-05-18T01:04:55.093990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:55.093990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4pciJOK4JheGvkg5Q7HbMwy1jtqivQkkxetRMH7QAOZo4DCzKYEHYdz5qwRMfT5vUxrzVW648/ILqzbam/aODg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:55.094603Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02258","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e21debeb2b6cf47ea06287a118f83a83659355a9280f8b79b2cc9fa5a4d67fc7","sha256:84c93e543270f78eabcda523df94b140a3a41e3b4f947caf3354458561f3b08f"],"state_sha256":"e645d306bd20dd52c6a4d16b52a9110414f18ace16bfa60aa7a1ca49d5ae7254"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gU6LQ0fCCm5KZPi+sONMg/ZdE3CsxGjzma6z68XujfIZiImgTKAPwaWm/VMzjDETc3LGz6ZUicBVxdDUglAFCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:55:56.661275Z","bundle_sha256":"9475c4d4d6c3e3e9667a0c950dd8454f89d1659ef0c1641d97a287991e2db668"}}