{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IXCSBZ4CV57CI5YCHHNQWDM44F","short_pith_number":"pith:IXCSBZ4C","canonical_record":{"source":{"id":"1212.4560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-19T02:53:41Z","cross_cats_sorted":["cs.NA","math.PR"],"title_canon_sha256":"caebed05c8ce21e915d2dac004711b733d381acf0e24299050a7cf7458318f9c","abstract_canon_sha256":"4701f8644b91b9a58ebb2a59590968b33a6270c4586a1573aa135845cda7d8ba"},"schema_version":"1.0"},"canonical_sha256":"45c520e782af7e24770239db0b0d9ce17d8060f864d3acc68007cbc25fa070cd","source":{"kind":"arxiv","id":"1212.4560","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4560","created_at":"2026-05-18T03:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4560v2","created_at":"2026-05-18T03:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4560","created_at":"2026-05-18T03:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"IXCSBZ4CV57C","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IXCSBZ4CV57CI5YC","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IXCSBZ4C","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IXCSBZ4CV57CI5YCHHNQWDM44F","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-19T02:53:41Z","cross_cats_sorted":["cs.NA","math.PR"],"title_canon_sha256":"caebed05c8ce21e915d2dac004711b733d381acf0e24299050a7cf7458318f9c","abstract_canon_sha256":"4701f8644b91b9a58ebb2a59590968b33a6270c4586a1573aa135845cda7d8ba"},"schema_version":"1.0"},"canonical_sha256":"45c520e782af7e24770239db0b0d9ce17d8060f864d3acc68007cbc25fa070cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:52.160858Z","signature_b64":"Nw85o+QsF+NxOPGfCZfsolhT00hkF41rHXANuWcxuupDoMWpSpJpMe+FH5syj6FBADAaL1Gdv5aaIFpmvQb0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45c520e782af7e24770239db0b0d9ce17d8060f864d3acc68007cbc25fa070cd","last_reissued_at":"2026-05-18T03:37:52.160144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:52.160144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4560","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":"2026-05-18T03:37:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wvqG9/4Wh4oKz5VRj+zjPSI76HZt7l0DVJE7RX0waq+GlaSwJ0qo8HLu+iRuypavVR+/2uhG+czFWbc2pQXnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T13:18:56.702078Z"},"content_sha256":"7ce648d6b89f5002497580b62df5b828f87eb3dd4622a7796127a732de366f37","schema_version":"1.0","event_id":"sha256:7ce648d6b89f5002497580b62df5b828f87eb3dd4622a7796127a732de366f37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IXCSBZ4CV57CI5YCHHNQWDM44F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"More on the Power of Randomized Matrix Computations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Guoliang Qian, Victor Y. Pan","submitted_at":"2012-12-19T02:53:41Z","abstract_excerpt":"A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination with no pivoting as well as block Gaussian elimination, approximation of the leading and trailing singular spaces of an ill conditioned matrix, associated with its largest and smallest singular values, respectively, and approximation of this matrix by low-rank matrices, with further extensions to computing numerical ranks and the approximation of tensor decom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4560","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":"2026-05-18T03:37:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"udgW3wD1oecOg5nHhp4OJkZ5b/g5g+u/34lbxjJKQAinVEignAULHfXFS6QKlajHC8hUXG8IjwIwLpS3aqq0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T13:18:56.702456Z"},"content_sha256":"4f3a8871a324bca4bbee69aa6bb7c45212e73176b1a0fad431b2041db1eac3e1","schema_version":"1.0","event_id":"sha256:4f3a8871a324bca4bbee69aa6bb7c45212e73176b1a0fad431b2041db1eac3e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IXCSBZ4CV57CI5YCHHNQWDM44F/bundle.json","state_url":"https://pith.science/pith/IXCSBZ4CV57CI5YCHHNQWDM44F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IXCSBZ4CV57CI5YCHHNQWDM44F/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":"2026-06-11T13:18:56Z","links":{"resolver":"https://pith.science/pith/IXCSBZ4CV57CI5YCHHNQWDM44F","bundle":"https://pith.science/pith/IXCSBZ4CV57CI5YCHHNQWDM44F/bundle.json","state":"https://pith.science/pith/IXCSBZ4CV57CI5YCHHNQWDM44F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IXCSBZ4CV57CI5YCHHNQWDM44F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IXCSBZ4CV57CI5YCHHNQWDM44F","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":"4701f8644b91b9a58ebb2a59590968b33a6270c4586a1573aa135845cda7d8ba","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-19T02:53:41Z","title_canon_sha256":"caebed05c8ce21e915d2dac004711b733d381acf0e24299050a7cf7458318f9c"},"schema_version":"1.0","source":{"id":"1212.4560","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4560","created_at":"2026-05-18T03:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4560v2","created_at":"2026-05-18T03:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4560","created_at":"2026-05-18T03:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"IXCSBZ4CV57C","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IXCSBZ4CV57CI5YC","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IXCSBZ4C","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:4f3a8871a324bca4bbee69aa6bb7c45212e73176b1a0fad431b2041db1eac3e1","target":"graph","created_at":"2026-05-18T03:37:52Z","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":"A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination with no pivoting as well as block Gaussian elimination, approximation of the leading and trailing singular spaces of an ill conditioned matrix, associated with its largest and smallest singular values, respectively, and approximation of this matrix by low-rank matrices, with further extensions to computing numerical ranks and the approximation of tensor decom","authors_text":"Guoliang Qian, Victor Y. Pan","cross_cats":["cs.NA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-19T02:53:41Z","title":"More on the Power of Randomized Matrix Computations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4560","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":"sha256:7ce648d6b89f5002497580b62df5b828f87eb3dd4622a7796127a732de366f37","target":"record","created_at":"2026-05-18T03:37:52Z","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":"4701f8644b91b9a58ebb2a59590968b33a6270c4586a1573aa135845cda7d8ba","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-19T02:53:41Z","title_canon_sha256":"caebed05c8ce21e915d2dac004711b733d381acf0e24299050a7cf7458318f9c"},"schema_version":"1.0","source":{"id":"1212.4560","kind":"arxiv","version":2}},"canonical_sha256":"45c520e782af7e24770239db0b0d9ce17d8060f864d3acc68007cbc25fa070cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45c520e782af7e24770239db0b0d9ce17d8060f864d3acc68007cbc25fa070cd","first_computed_at":"2026-05-18T03:37:52.160144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:52.160144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nw85o+QsF+NxOPGfCZfsolhT00hkF41rHXANuWcxuupDoMWpSpJpMe+FH5syj6FBADAaL1Gdv5aaIFpmvQb0CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:52.160858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4560","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ce648d6b89f5002497580b62df5b828f87eb3dd4622a7796127a732de366f37","sha256:4f3a8871a324bca4bbee69aa6bb7c45212e73176b1a0fad431b2041db1eac3e1"],"state_sha256":"a379134854c327aa9340931fd27715f608c33e54c74d5531ba984367d6bcb618"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m4m3K6sLL9rj6/GLXrduBAevB5B1AvnmBhS1iAuZwDBNUubB/LPB4toa/xkO03NK+HLeJhMKNU0fobwyPDp1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T13:18:56.704766Z","bundle_sha256":"eb83efc98d731cada4c110a3d144952aee7165ef0571ba213471ef826588de8e"}}