{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3D5NZF7DOUF33XD6TYBZIKYKSO","short_pith_number":"pith:3D5NZF7D","canonical_record":{"source":{"id":"1504.05477","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-21T15:48:44Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"7f362566fb6675cbb299ee0a06108aaa80e92f2df41ea8a04e0e63c42f34ea9c","abstract_canon_sha256":"2e4f1ee54fe12588e955fa8a63384ab7226ba32176d86e694d6e3b60393ab19f"},"schema_version":"1.0"},"canonical_sha256":"d8fadc97e3750bbddc7e9e03942b0a93811660cc6ed5c20516a248c96246817d","source":{"kind":"arxiv","id":"1504.05477","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05477","created_at":"2026-05-18T01:28:25Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05477v4","created_at":"2026-05-18T01:28:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05477","created_at":"2026-05-18T01:28:25Z"},{"alias_kind":"pith_short_12","alias_value":"3D5NZF7DOUF3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3D5NZF7DOUF33XD6","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3D5NZF7D","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3D5NZF7DOUF33XD6TYBZIKYKSO","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05477","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-21T15:48:44Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"7f362566fb6675cbb299ee0a06108aaa80e92f2df41ea8a04e0e63c42f34ea9c","abstract_canon_sha256":"2e4f1ee54fe12588e955fa8a63384ab7226ba32176d86e694d6e3b60393ab19f"},"schema_version":"1.0"},"canonical_sha256":"d8fadc97e3750bbddc7e9e03942b0a93811660cc6ed5c20516a248c96246817d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:25.715689Z","signature_b64":"dqIfRf1jBXUzsl4RvXDAqrkaZIBbnHY0ThzLo3Gj19n5LbZ8q0Tw8syTSYo6W8S6Yc6M5WdxOvA348GCEZhEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8fadc97e3750bbddc7e9e03942b0a93811660cc6ed5c20516a248c96246817d","last_reissued_at":"2026-05-18T01:28:25.715095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:25.715095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05477","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"toSG6do1smIxSALy9Q1ITXsq3BscL1H7oLPZediGeENvAOpIQmt+4fsMw3GtZ9tBlQSXVG3SkG0obCumQvTEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:00:56.159259Z"},"content_sha256":"32ee8b4445935988c0ed9ec97db38f152579453e57132622a50de2704e4bb18e","schema_version":"1.0","event_id":"sha256:32ee8b4445935988c0ed9ec97db38f152579453e57132622a50de2704e4bb18e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3D5NZF7DOUF33XD6TYBZIKYKSO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"cs.DS","authors_text":"Cameron Musco, Christopher Musco","submitted_at":"2015-04-21T15:48:44Z","abstract_excerpt":"Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate than simpler sketching algorithms, yet still converges quickly for any matrix, independently of singular value gaps. After $\\tilde{O}(1/\\epsilon)$ iterations, it gives a low-rank approximation within $(1+\\epsilon)$ of optimal for spectral norm error.\n  We give the first provable runtime improvement on Simultaneous Iteration: a simple randomized block Krylov me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05477","kind":"arxiv","version":4},"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":"2026-05-18T01:28:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DX9LjwnuhpG6sxCS0CNedOF3EFz/Xwsca3ASJHAczSpjPWbMp9RnYUrbf5m/9tXT0wABJcjdjxPbUqgyjftaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:00:56.159628Z"},"content_sha256":"7bb94241d2c4c3b213d2b6e91597fdf2d3de8c114205b21128d46b2308885bde","schema_version":"1.0","event_id":"sha256:7bb94241d2c4c3b213d2b6e91597fdf2d3de8c114205b21128d46b2308885bde"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3D5NZF7DOUF33XD6TYBZIKYKSO/bundle.json","state_url":"https://pith.science/pith/3D5NZF7DOUF33XD6TYBZIKYKSO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3D5NZF7DOUF33XD6TYBZIKYKSO/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":"2026-06-20T09:00:56Z","links":{"resolver":"https://pith.science/pith/3D5NZF7DOUF33XD6TYBZIKYKSO","bundle":"https://pith.science/pith/3D5NZF7DOUF33XD6TYBZIKYKSO/bundle.json","state":"https://pith.science/pith/3D5NZF7DOUF33XD6TYBZIKYKSO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3D5NZF7DOUF33XD6TYBZIKYKSO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3D5NZF7DOUF33XD6TYBZIKYKSO","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":"2e4f1ee54fe12588e955fa8a63384ab7226ba32176d86e694d6e3b60393ab19f","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-21T15:48:44Z","title_canon_sha256":"7f362566fb6675cbb299ee0a06108aaa80e92f2df41ea8a04e0e63c42f34ea9c"},"schema_version":"1.0","source":{"id":"1504.05477","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05477","created_at":"2026-05-18T01:28:25Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05477v4","created_at":"2026-05-18T01:28:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05477","created_at":"2026-05-18T01:28:25Z"},{"alias_kind":"pith_short_12","alias_value":"3D5NZF7DOUF3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3D5NZF7DOUF33XD6","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3D5NZF7D","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:7bb94241d2c4c3b213d2b6e91597fdf2d3de8c114205b21128d46b2308885bde","target":"graph","created_at":"2026-05-18T01:28:25Z","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":"Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate than simpler sketching algorithms, yet still converges quickly for any matrix, independently of singular value gaps. After $\\tilde{O}(1/\\epsilon)$ iterations, it gives a low-rank approximation within $(1+\\epsilon)$ of optimal for spectral norm error.\n  We give the first provable runtime improvement on Simultaneous Iteration: a simple randomized block Krylov me","authors_text":"Cameron Musco, Christopher Musco","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-21T15:48:44Z","title":"Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05477","kind":"arxiv","version":4},"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":"sha256:32ee8b4445935988c0ed9ec97db38f152579453e57132622a50de2704e4bb18e","target":"record","created_at":"2026-05-18T01:28:25Z","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":"2e4f1ee54fe12588e955fa8a63384ab7226ba32176d86e694d6e3b60393ab19f","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-21T15:48:44Z","title_canon_sha256":"7f362566fb6675cbb299ee0a06108aaa80e92f2df41ea8a04e0e63c42f34ea9c"},"schema_version":"1.0","source":{"id":"1504.05477","kind":"arxiv","version":4}},"canonical_sha256":"d8fadc97e3750bbddc7e9e03942b0a93811660cc6ed5c20516a248c96246817d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8fadc97e3750bbddc7e9e03942b0a93811660cc6ed5c20516a248c96246817d","first_computed_at":"2026-05-18T01:28:25.715095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:25.715095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dqIfRf1jBXUzsl4RvXDAqrkaZIBbnHY0ThzLo3Gj19n5LbZ8q0Tw8syTSYo6W8S6Yc6M5WdxOvA348GCEZhEDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:25.715689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05477","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32ee8b4445935988c0ed9ec97db38f152579453e57132622a50de2704e4bb18e","sha256:7bb94241d2c4c3b213d2b6e91597fdf2d3de8c114205b21128d46b2308885bde"],"state_sha256":"a03a508fc6fba11cd738733f111d905bda02643991984041d8855fed99fbda64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jIqT1Iapg595Ci8Aj+fVwJ74AgSQ3//WFrJhQlL+ZidC/jBtK1x+WIUrCVzb6aBerbbSBJl9ZnEXr/RN5BFcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T09:00:56.161510Z","bundle_sha256":"beadd7701567adab534fedeb6e5bc4bf8efd30f74a6b51aaa4fd259cfef88681"}}