{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PQ6B7YP5MQIAY27MEXSA5GINUF","short_pith_number":"pith:PQ6B7YP5","canonical_record":{"source":{"id":"1110.0166","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-02T10:26:37Z","cross_cats_sorted":[],"title_canon_sha256":"11701f327c14a1d6b68e22ad6069a626a109962db711b237f60b417bf1fe8be2","abstract_canon_sha256":"61d21e484755df2be46e1c1715266d0741386d98c1809b038eaac5f8a7ce339b"},"schema_version":"1.0"},"canonical_sha256":"7c3c1fe1fd64100c6bec25e40e990da177200232f157efba6f63a0174017e867","source":{"kind":"arxiv","id":"1110.0166","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0166","created_at":"2026-05-18T02:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0166v3","created_at":"2026-05-18T02:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0166","created_at":"2026-05-18T02:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"PQ6B7YP5MQIA","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PQ6B7YP5MQIAY27M","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PQ6B7YP5","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PQ6B7YP5MQIAY27MEXSA5GINUF","target":"record","payload":{"canonical_record":{"source":{"id":"1110.0166","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-02T10:26:37Z","cross_cats_sorted":[],"title_canon_sha256":"11701f327c14a1d6b68e22ad6069a626a109962db711b237f60b417bf1fe8be2","abstract_canon_sha256":"61d21e484755df2be46e1c1715266d0741386d98c1809b038eaac5f8a7ce339b"},"schema_version":"1.0"},"canonical_sha256":"7c3c1fe1fd64100c6bec25e40e990da177200232f157efba6f63a0174017e867","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:35.922448Z","signature_b64":"w8olqWEV0rIgXf7Gi/yl10i4+iAEKV3TUfeDhy916CZeeSTDKCczSZ0LZ9k7G0NH4hHYxiTXveQAAHFKiIkKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c3c1fe1fd64100c6bec25e40e990da177200232f157efba6f63a0174017e867","last_reissued_at":"2026-05-18T02:23:35.921674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:35.921674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.0166","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":"2026-05-18T02:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T1Iyap9eJFw6wyy3Ce257dILuZ2akKF6hTjkIxBtDJQOem73300ooZklIycvIoZlgs33xcfPEPNwH28pbY35Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:17:40.638874Z"},"content_sha256":"faaf893a106d37e07fcb010eb8e04b9499e0fb36a7d8300242e84006462daa49","schema_version":"1.0","event_id":"sha256:faaf893a106d37e07fcb010eb8e04b9499e0fb36a7d8300242e84006462daa49"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PQ6B7YP5MQIAY27MEXSA5GINUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Condition Number of the Total Least Squares Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bingyu Li, Zhongxiao Jia","submitted_at":"2011-10-02T10:26:37Z","abstract_excerpt":"This paper concerns singular value decomposition (SVD)-based computable formulas and bounds for the condition number of the Total Least Squares (TLS) problem. For the TLS problem with the coefficient matrix $A$ and the right-hand side $b$, a new closed formula is presented for the condition number. Unlike an important result in the literature that uses the SVDs of both $A$ and $[A,\\ b]$, our formula only requires the SVD of $[A,\\ b]$. Based on the closed formula, both lower and upper bounds for the condition number are derived. It is proved that they are always sharp and estimate the condition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0166","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":"2026-05-18T02:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a/+gkDEGqThaadc2GCA4zjs02UHaA0Zt/dulgd+yGLBDnqSUxUj51N5kyO1a6c7nckfMiZBb2IFBRnc4gIhQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:17:40.639225Z"},"content_sha256":"e4a2b9bb047983bc14f037c61fa6c235f0a92d5ac10a6a4cfe6cfe36034bb05d","schema_version":"1.0","event_id":"sha256:e4a2b9bb047983bc14f037c61fa6c235f0a92d5ac10a6a4cfe6cfe36034bb05d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQ6B7YP5MQIAY27MEXSA5GINUF/bundle.json","state_url":"https://pith.science/pith/PQ6B7YP5MQIAY27MEXSA5GINUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQ6B7YP5MQIAY27MEXSA5GINUF/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":"2026-06-26T04:17:40Z","links":{"resolver":"https://pith.science/pith/PQ6B7YP5MQIAY27MEXSA5GINUF","bundle":"https://pith.science/pith/PQ6B7YP5MQIAY27MEXSA5GINUF/bundle.json","state":"https://pith.science/pith/PQ6B7YP5MQIAY27MEXSA5GINUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQ6B7YP5MQIAY27MEXSA5GINUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PQ6B7YP5MQIAY27MEXSA5GINUF","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":"61d21e484755df2be46e1c1715266d0741386d98c1809b038eaac5f8a7ce339b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-02T10:26:37Z","title_canon_sha256":"11701f327c14a1d6b68e22ad6069a626a109962db711b237f60b417bf1fe8be2"},"schema_version":"1.0","source":{"id":"1110.0166","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0166","created_at":"2026-05-18T02:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0166v3","created_at":"2026-05-18T02:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0166","created_at":"2026-05-18T02:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"PQ6B7YP5MQIA","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PQ6B7YP5MQIAY27M","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PQ6B7YP5","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:e4a2b9bb047983bc14f037c61fa6c235f0a92d5ac10a6a4cfe6cfe36034bb05d","target":"graph","created_at":"2026-05-18T02:23:35Z","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":"This paper concerns singular value decomposition (SVD)-based computable formulas and bounds for the condition number of the Total Least Squares (TLS) problem. For the TLS problem with the coefficient matrix $A$ and the right-hand side $b$, a new closed formula is presented for the condition number. Unlike an important result in the literature that uses the SVDs of both $A$ and $[A,\\ b]$, our formula only requires the SVD of $[A,\\ b]$. Based on the closed formula, both lower and upper bounds for the condition number are derived. It is proved that they are always sharp and estimate the condition","authors_text":"Bingyu Li, Zhongxiao Jia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-02T10:26:37Z","title":"On the Condition Number of the Total Least Squares Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0166","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:faaf893a106d37e07fcb010eb8e04b9499e0fb36a7d8300242e84006462daa49","target":"record","created_at":"2026-05-18T02:23:35Z","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":"61d21e484755df2be46e1c1715266d0741386d98c1809b038eaac5f8a7ce339b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-02T10:26:37Z","title_canon_sha256":"11701f327c14a1d6b68e22ad6069a626a109962db711b237f60b417bf1fe8be2"},"schema_version":"1.0","source":{"id":"1110.0166","kind":"arxiv","version":3}},"canonical_sha256":"7c3c1fe1fd64100c6bec25e40e990da177200232f157efba6f63a0174017e867","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c3c1fe1fd64100c6bec25e40e990da177200232f157efba6f63a0174017e867","first_computed_at":"2026-05-18T02:23:35.921674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:35.921674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w8olqWEV0rIgXf7Gi/yl10i4+iAEKV3TUfeDhy916CZeeSTDKCczSZ0LZ9k7G0NH4hHYxiTXveQAAHFKiIkKCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:35.922448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.0166","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:faaf893a106d37e07fcb010eb8e04b9499e0fb36a7d8300242e84006462daa49","sha256:e4a2b9bb047983bc14f037c61fa6c235f0a92d5ac10a6a4cfe6cfe36034bb05d"],"state_sha256":"09d615f5399888395feafe7750e044056a84e2773d6293f5c42870e4628ddcb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dhGVsXqPkvTy2fICAnLij+d7zh1TYx8qu7KicQeFQnJsYv53yRhSn9llzC65emtUpdphwyFJU2SYoNvN8arDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T04:17:40.641449Z","bundle_sha256":"bd208e8c1bde2c6d3bf059c0093dd72ad6b0c9828074d03e4773315ccf687dd2"}}