{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZPT5ZQVB6UFWEAS34LXGZQPS7P","short_pith_number":"pith:ZPT5ZQVB","canonical_record":{"source":{"id":"1406.5802","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-23T03:12:28Z","cross_cats_sorted":[],"title_canon_sha256":"aed608171624225d4b89c926973eceac9eb3027005e5e4ca72171eff508469a5","abstract_canon_sha256":"28c310811bff637217dae41896395b29490f6f9495cfab237b8ed5ea58edc916"},"schema_version":"1.0"},"canonical_sha256":"cbe7dcc2a1f50b62025be2ee6cc1f2fbfb7b736084b899ffe2da616dd1b675e0","source":{"kind":"arxiv","id":"1406.5802","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5802","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5802v2","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5802","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZPT5ZQVB6UFW","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZPT5ZQVB6UFWEAS3","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZPT5ZQVB","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZPT5ZQVB6UFWEAS34LXGZQPS7P","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5802","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-23T03:12:28Z","cross_cats_sorted":[],"title_canon_sha256":"aed608171624225d4b89c926973eceac9eb3027005e5e4ca72171eff508469a5","abstract_canon_sha256":"28c310811bff637217dae41896395b29490f6f9495cfab237b8ed5ea58edc916"},"schema_version":"1.0"},"canonical_sha256":"cbe7dcc2a1f50b62025be2ee6cc1f2fbfb7b736084b899ffe2da616dd1b675e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:03.861256Z","signature_b64":"gGmpja3QTNVN4W/Qvf+ke7Pz+srBToVl1emnOnMe450OU3+VAU3YAHdMefLIC2t/M+oCkRYlz9HBarlifs6WDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbe7dcc2a1f50b62025be2ee6cc1f2fbfb7b736084b899ffe2da616dd1b675e0","last_reissued_at":"2026-05-18T02:31:03.860657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:03.860657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5802","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":"2026-05-18T02:31:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"icz38GgxaweFXXKKV26z+DSvMmzOUbfr3KBcqQXwD7vHSHHngBos28XcJ2GQXb+aAQ+1WGgFQo+swH1RZeCcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:54:54.139274Z"},"content_sha256":"55d64f94b13d61d89f42e7de40aaa8453b0bcf24863314d54831b80fbeec47e2","schema_version":"1.0","event_id":"sha256:55d64f94b13d61d89f42e7de40aaa8453b0bcf24863314d54831b80fbeec47e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZPT5ZQVB6UFWEAS34LXGZQPS7P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random Multipliers Numerically Stabilize Gaussian and Block Gaussian Elimination: Proofs and an Extension to Low-rank Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Guoliang Qian, Victor Y. Pan, Xiaodong Yan","submitted_at":"2014-06-23T03:12:28Z","abstract_excerpt":"We prove that standard Gaussian random multipliers are expected to numerically stabilize both Gaussian elimination with no pivoting and block Gaussian elimination. Moreover we prove that such a multiplier (even without the customary oversampling) is expected to support low-rank approximation of a matrix. Our test results are in good accordance with this analysis. Empirically random circulant or Toeplitz multipliers are as efficient as Gaussian ones, but their formal support is more problematic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5802","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":"2026-05-18T02:31:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owQOCVcvOycpUwfuxbjlQHF5LL80C79qF67Elvk/H9YCDO5YSXXR9SVpir8G5hybvrUEPJO92tVyRTZUYZG+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:54:54.140064Z"},"content_sha256":"dbdbf0fd0142ff78683ea8963d2af960ded72f715e5144791102429e9397726c","schema_version":"1.0","event_id":"sha256:dbdbf0fd0142ff78683ea8963d2af960ded72f715e5144791102429e9397726c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZPT5ZQVB6UFWEAS34LXGZQPS7P/bundle.json","state_url":"https://pith.science/pith/ZPT5ZQVB6UFWEAS34LXGZQPS7P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZPT5ZQVB6UFWEAS34LXGZQPS7P/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":"2026-06-09T06:54:54Z","links":{"resolver":"https://pith.science/pith/ZPT5ZQVB6UFWEAS34LXGZQPS7P","bundle":"https://pith.science/pith/ZPT5ZQVB6UFWEAS34LXGZQPS7P/bundle.json","state":"https://pith.science/pith/ZPT5ZQVB6UFWEAS34LXGZQPS7P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZPT5ZQVB6UFWEAS34LXGZQPS7P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZPT5ZQVB6UFWEAS34LXGZQPS7P","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":"28c310811bff637217dae41896395b29490f6f9495cfab237b8ed5ea58edc916","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-23T03:12:28Z","title_canon_sha256":"aed608171624225d4b89c926973eceac9eb3027005e5e4ca72171eff508469a5"},"schema_version":"1.0","source":{"id":"1406.5802","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5802","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5802v2","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5802","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZPT5ZQVB6UFW","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZPT5ZQVB6UFWEAS3","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZPT5ZQVB","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:dbdbf0fd0142ff78683ea8963d2af960ded72f715e5144791102429e9397726c","target":"graph","created_at":"2026-05-18T02:31:03Z","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 prove that standard Gaussian random multipliers are expected to numerically stabilize both Gaussian elimination with no pivoting and block Gaussian elimination. Moreover we prove that such a multiplier (even without the customary oversampling) is expected to support low-rank approximation of a matrix. Our test results are in good accordance with this analysis. Empirically random circulant or Toeplitz multipliers are as efficient as Gaussian ones, but their formal support is more problematic.","authors_text":"Guoliang Qian, Victor Y. Pan, Xiaodong Yan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-23T03:12:28Z","title":"Random Multipliers Numerically Stabilize Gaussian and Block Gaussian Elimination: Proofs and an Extension to Low-rank Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5802","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":"sha256:55d64f94b13d61d89f42e7de40aaa8453b0bcf24863314d54831b80fbeec47e2","target":"record","created_at":"2026-05-18T02:31:03Z","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":"28c310811bff637217dae41896395b29490f6f9495cfab237b8ed5ea58edc916","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-23T03:12:28Z","title_canon_sha256":"aed608171624225d4b89c926973eceac9eb3027005e5e4ca72171eff508469a5"},"schema_version":"1.0","source":{"id":"1406.5802","kind":"arxiv","version":2}},"canonical_sha256":"cbe7dcc2a1f50b62025be2ee6cc1f2fbfb7b736084b899ffe2da616dd1b675e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbe7dcc2a1f50b62025be2ee6cc1f2fbfb7b736084b899ffe2da616dd1b675e0","first_computed_at":"2026-05-18T02:31:03.860657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:03.860657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gGmpja3QTNVN4W/Qvf+ke7Pz+srBToVl1emnOnMe450OU3+VAU3YAHdMefLIC2t/M+oCkRYlz9HBarlifs6WDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:03.861256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5802","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55d64f94b13d61d89f42e7de40aaa8453b0bcf24863314d54831b80fbeec47e2","sha256:dbdbf0fd0142ff78683ea8963d2af960ded72f715e5144791102429e9397726c"],"state_sha256":"a553ea31160d90da8e91ad1e0b1016d8a2d59b9a55d49606521dab223750e7bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YGFxI6+wSwjz2hXq79DyvEv56nh7/9siiA1EmC/6pKgHpao2DWvTfSAKTdYgPzZDfbwgI9OYGoWRy3G+JiRmDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:54:54.144190Z","bundle_sha256":"4849eb356f0844fc22fb7e1d8a8028e46923c0c3eb335c9d1be6e70f9feee3c7"}}