{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:I2ZR7NSAG7ZTTZ7BQ6E5DAFKQH","short_pith_number":"pith:I2ZR7NSA","canonical_record":{"source":{"id":"1412.5864","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-18T14:13:35Z","cross_cats_sorted":[],"title_canon_sha256":"5b05d4f2e481fb5d54c124a9e277819f19c729237d3af9cb43640dfe61c30b5d","abstract_canon_sha256":"822bec2a1e735ed049b3c1a1fe7f441e807664f3fc99ed8ce03ac8d52fa54a52"},"schema_version":"1.0"},"canonical_sha256":"46b31fb64037f339e7e18789d180aa81e53c8653ab2f76ae712a9af730fae279","source":{"kind":"arxiv","id":"1412.5864","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5864","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5864v3","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5864","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"pith_short_12","alias_value":"I2ZR7NSAG7ZT","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I2ZR7NSAG7ZTTZ7B","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I2ZR7NSA","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:I2ZR7NSAG7ZTTZ7BQ6E5DAFKQH","target":"record","payload":{"canonical_record":{"source":{"id":"1412.5864","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-18T14:13:35Z","cross_cats_sorted":[],"title_canon_sha256":"5b05d4f2e481fb5d54c124a9e277819f19c729237d3af9cb43640dfe61c30b5d","abstract_canon_sha256":"822bec2a1e735ed049b3c1a1fe7f441e807664f3fc99ed8ce03ac8d52fa54a52"},"schema_version":"1.0"},"canonical_sha256":"46b31fb64037f339e7e18789d180aa81e53c8653ab2f76ae712a9af730fae279","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:00.566720Z","signature_b64":"wRhzrnUo71nBxobKj7tgn/rRuZtpLWbxceFqIWFc8FLbWIesrVmsmZYTjampfJViyMZcsFHFJcq4mCxeoBszCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46b31fb64037f339e7e18789d180aa81e53c8653ab2f76ae712a9af730fae279","last_reissued_at":"2026-05-18T01:19:00.566147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:00.566147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.5864","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":"2026-05-18T01:19:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PeKLr2qfUH6y3qRjlANMfgkWiXFCRGuLQiycJ40Nan3/ONZnzzw4BffRUBYwEcPS2IaOpY4ovSCoGVekWqc8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:01:28.432623Z"},"content_sha256":"5993024f28ae33332d64f416969ced9074ec4d3c9fb876e9cb20c523bdc73abf","schema_version":"1.0","event_id":"sha256:5993024f28ae33332d64f416969ced9074ec4d3c9fb876e9cb20c523bdc73abf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:I2ZR7NSAG7ZTTZ7BQ6E5DAFKQH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Studies of Randomized Augmentation and Additive Preprocessing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Liang Zhao, Victor Y. Pan","submitted_at":"2014-12-18T14:13:35Z","abstract_excerpt":"1. A standard Gaussian random matrix has full rank with probability 1 and is well-conditioned with a probability quite close to 1 and converging to 1 fast as the matrix deviates from square shape and becomes more rectangular. 2. If we append sufficiently many standard Gaussian random rows or columns to any normalized matrix A, then the augmented matrix has full rank with probability 1 and is well-conditioned with a probability close to 1, even if the matrix A is rank deficient or ill-conditioned. 3. We specify and prove these properties of augmentation and extend them to additive preprocessing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5864","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":"2026-05-18T01:19:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TW1mpInioAQEVJflFoc+b2A0w4oFhfaUog2Ssdi2BCMatG5XIfRSQEGQ8fPO+xCOxPeLwP51ooCzWQbwdyh+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:01:28.433303Z"},"content_sha256":"703715cb02544751c8ee63a7af5da5c961af766ce1dffc4d39377b30209ee41e","schema_version":"1.0","event_id":"sha256:703715cb02544751c8ee63a7af5da5c961af766ce1dffc4d39377b30209ee41e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I2ZR7NSAG7ZTTZ7BQ6E5DAFKQH/bundle.json","state_url":"https://pith.science/pith/I2ZR7NSAG7ZTTZ7BQ6E5DAFKQH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I2ZR7NSAG7ZTTZ7BQ6E5DAFKQH/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":"2026-06-07T22:01:28Z","links":{"resolver":"https://pith.science/pith/I2ZR7NSAG7ZTTZ7BQ6E5DAFKQH","bundle":"https://pith.science/pith/I2ZR7NSAG7ZTTZ7BQ6E5DAFKQH/bundle.json","state":"https://pith.science/pith/I2ZR7NSAG7ZTTZ7BQ6E5DAFKQH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I2ZR7NSAG7ZTTZ7BQ6E5DAFKQH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I2ZR7NSAG7ZTTZ7BQ6E5DAFKQH","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":"822bec2a1e735ed049b3c1a1fe7f441e807664f3fc99ed8ce03ac8d52fa54a52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-18T14:13:35Z","title_canon_sha256":"5b05d4f2e481fb5d54c124a9e277819f19c729237d3af9cb43640dfe61c30b5d"},"schema_version":"1.0","source":{"id":"1412.5864","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5864","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5864v3","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5864","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"pith_short_12","alias_value":"I2ZR7NSAG7ZT","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I2ZR7NSAG7ZTTZ7B","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I2ZR7NSA","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:703715cb02544751c8ee63a7af5da5c961af766ce1dffc4d39377b30209ee41e","target":"graph","created_at":"2026-05-18T01:19:00Z","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":"1. A standard Gaussian random matrix has full rank with probability 1 and is well-conditioned with a probability quite close to 1 and converging to 1 fast as the matrix deviates from square shape and becomes more rectangular. 2. If we append sufficiently many standard Gaussian random rows or columns to any normalized matrix A, then the augmented matrix has full rank with probability 1 and is well-conditioned with a probability close to 1, even if the matrix A is rank deficient or ill-conditioned. 3. We specify and prove these properties of augmentation and extend them to additive preprocessing","authors_text":"Liang Zhao, Victor Y. Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-18T14:13:35Z","title":"New Studies of Randomized Augmentation and Additive Preprocessing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5864","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":"sha256:5993024f28ae33332d64f416969ced9074ec4d3c9fb876e9cb20c523bdc73abf","target":"record","created_at":"2026-05-18T01:19:00Z","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":"822bec2a1e735ed049b3c1a1fe7f441e807664f3fc99ed8ce03ac8d52fa54a52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-18T14:13:35Z","title_canon_sha256":"5b05d4f2e481fb5d54c124a9e277819f19c729237d3af9cb43640dfe61c30b5d"},"schema_version":"1.0","source":{"id":"1412.5864","kind":"arxiv","version":3}},"canonical_sha256":"46b31fb64037f339e7e18789d180aa81e53c8653ab2f76ae712a9af730fae279","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46b31fb64037f339e7e18789d180aa81e53c8653ab2f76ae712a9af730fae279","first_computed_at":"2026-05-18T01:19:00.566147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:00.566147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wRhzrnUo71nBxobKj7tgn/rRuZtpLWbxceFqIWFc8FLbWIesrVmsmZYTjampfJViyMZcsFHFJcq4mCxeoBszCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:00.566720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5864","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5993024f28ae33332d64f416969ced9074ec4d3c9fb876e9cb20c523bdc73abf","sha256:703715cb02544751c8ee63a7af5da5c961af766ce1dffc4d39377b30209ee41e"],"state_sha256":"f75548fa1503e0d3a37c23db6f00d7ecfef09150a79e04f6a087ae3af7b22243"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"39lhdML0+UGbRjW7VMZFPBefRBcAfnC5vfLr2On9szpz4brtumdBKZ/sZ5KV9n97GcRwGfkV/UobSqXTu88zDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:01:28.437064Z","bundle_sha256":"eb0c2b05bcf1db11d8e3b712abde0aa73ab4717ae18fb2c3c67a92213c9d0aaf"}}