{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UPX6A3CMNC4VLRKVMXBMZACSND","short_pith_number":"pith:UPX6A3CM","canonical_record":{"source":{"id":"1412.1901","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T06:42:02Z","cross_cats_sorted":[],"title_canon_sha256":"ad5ba91c7003b81c22051f0e2b9da274816116380779682c715a9a53ed65f92c","abstract_canon_sha256":"bfbab4b6ca4927d3874d56daf78fb738c2747b53b393ac3d57113c887f0ad69f"},"schema_version":"1.0"},"canonical_sha256":"a3efe06c4c68b955c55565c2cc805268df7ba8b73897ad1ef91b9bd36a3cab5f","source":{"kind":"arxiv","id":"1412.1901","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1901","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1901v3","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1901","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"UPX6A3CMNC4V","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UPX6A3CMNC4VLRKV","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UPX6A3CM","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UPX6A3CMNC4VLRKVMXBMZACSND","target":"record","payload":{"canonical_record":{"source":{"id":"1412.1901","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T06:42:02Z","cross_cats_sorted":[],"title_canon_sha256":"ad5ba91c7003b81c22051f0e2b9da274816116380779682c715a9a53ed65f92c","abstract_canon_sha256":"bfbab4b6ca4927d3874d56daf78fb738c2747b53b393ac3d57113c887f0ad69f"},"schema_version":"1.0"},"canonical_sha256":"a3efe06c4c68b955c55565c2cc805268df7ba8b73897ad1ef91b9bd36a3cab5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:47.392779Z","signature_b64":"X+TdDasskovgCylw9sUEDBVQznvdpOSKP2w05tFxX5hvzgRCCTfB0CYXOaCGRG4sYy0CNdG+mMQ94iSlitT6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3efe06c4c68b955c55565c2cc805268df7ba8b73897ad1ef91b9bd36a3cab5f","last_reissued_at":"2026-05-18T02:28:47.392353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:47.392353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.1901","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":"2026-05-18T02:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4XCOkWBv+Dw/oV6smPibE+lfOyodH4DnHPbKIBN9AhUVUAdS+nVCIZENGmsEX0ODsl9YEGS560GgLaHQKezEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:34:13.632462Z"},"content_sha256":"606e9c2c38367ee5e82984d8c5fb717343a8385f6a48d7302575813a699f9119","schema_version":"1.0","event_id":"sha256:606e9c2c38367ee5e82984d8c5fb717343a8385f6a48d7302575813a699f9119"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UPX6A3CMNC4VLRKVMXBMZACSND","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Results on Regularization of LSQR and CGLS for Large-Scale Discrete Ill-Posed Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Yi Huang, Zhongxiao Jia","submitted_at":"2014-12-05T06:42:02Z","abstract_excerpt":"For large-scale discrete ill-posed problems, LSQR, a Lanczos bidiagonalization process based Krylov method, is most often used. It is well known that LSQR has natural regularizing properties, where the number of iterations plays the role of the regularization parameter. In this paper, for severely and moderately ill-posed problems, we establish quantitative bounds for the distance between the $k$-dimensional Krylov subspace and the subspace spanned by $k$ dominant right singular vectors. They show that the $k$-dimensional Krylov subspace may capture the $k$ dominant right singular vectors for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1901","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":"2026-05-18T02:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nF3ATx5QdQdNuZeKBnht9RIa6whmZhjUXQ4r+ZsIpHbftvukkwQhztecBADj53N+a/+GDAjFrBmdHgars547Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:34:13.632814Z"},"content_sha256":"b6528252268425e4f46a0d1f4949397e09f7beb17c8dd59bdae81d4fb5d8ae41","schema_version":"1.0","event_id":"sha256:b6528252268425e4f46a0d1f4949397e09f7beb17c8dd59bdae81d4fb5d8ae41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPX6A3CMNC4VLRKVMXBMZACSND/bundle.json","state_url":"https://pith.science/pith/UPX6A3CMNC4VLRKVMXBMZACSND/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPX6A3CMNC4VLRKVMXBMZACSND/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":"2026-05-28T08:34:13Z","links":{"resolver":"https://pith.science/pith/UPX6A3CMNC4VLRKVMXBMZACSND","bundle":"https://pith.science/pith/UPX6A3CMNC4VLRKVMXBMZACSND/bundle.json","state":"https://pith.science/pith/UPX6A3CMNC4VLRKVMXBMZACSND/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPX6A3CMNC4VLRKVMXBMZACSND/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UPX6A3CMNC4VLRKVMXBMZACSND","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":"bfbab4b6ca4927d3874d56daf78fb738c2747b53b393ac3d57113c887f0ad69f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T06:42:02Z","title_canon_sha256":"ad5ba91c7003b81c22051f0e2b9da274816116380779682c715a9a53ed65f92c"},"schema_version":"1.0","source":{"id":"1412.1901","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1901","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1901v3","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1901","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"UPX6A3CMNC4V","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UPX6A3CMNC4VLRKV","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UPX6A3CM","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:b6528252268425e4f46a0d1f4949397e09f7beb17c8dd59bdae81d4fb5d8ae41","target":"graph","created_at":"2026-05-18T02:28:47Z","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":"For large-scale discrete ill-posed problems, LSQR, a Lanczos bidiagonalization process based Krylov method, is most often used. It is well known that LSQR has natural regularizing properties, where the number of iterations plays the role of the regularization parameter. In this paper, for severely and moderately ill-posed problems, we establish quantitative bounds for the distance between the $k$-dimensional Krylov subspace and the subspace spanned by $k$ dominant right singular vectors. They show that the $k$-dimensional Krylov subspace may capture the $k$ dominant right singular vectors for ","authors_text":"Yi Huang, Zhongxiao Jia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T06:42:02Z","title":"Some Results on Regularization of LSQR and CGLS for Large-Scale Discrete Ill-Posed Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1901","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":"sha256:606e9c2c38367ee5e82984d8c5fb717343a8385f6a48d7302575813a699f9119","target":"record","created_at":"2026-05-18T02:28:47Z","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":"bfbab4b6ca4927d3874d56daf78fb738c2747b53b393ac3d57113c887f0ad69f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T06:42:02Z","title_canon_sha256":"ad5ba91c7003b81c22051f0e2b9da274816116380779682c715a9a53ed65f92c"},"schema_version":"1.0","source":{"id":"1412.1901","kind":"arxiv","version":3}},"canonical_sha256":"a3efe06c4c68b955c55565c2cc805268df7ba8b73897ad1ef91b9bd36a3cab5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3efe06c4c68b955c55565c2cc805268df7ba8b73897ad1ef91b9bd36a3cab5f","first_computed_at":"2026-05-18T02:28:47.392353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:47.392353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X+TdDasskovgCylw9sUEDBVQznvdpOSKP2w05tFxX5hvzgRCCTfB0CYXOaCGRG4sYy0CNdG+mMQ94iSlitT6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:47.392779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1901","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:606e9c2c38367ee5e82984d8c5fb717343a8385f6a48d7302575813a699f9119","sha256:b6528252268425e4f46a0d1f4949397e09f7beb17c8dd59bdae81d4fb5d8ae41"],"state_sha256":"8c2549adfc1bcc4d86beed39cf250a43925aa9966c495e5f258f620583c61d3a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9aNoxMo5aa9C+qDF2c3mhoA+kHdMkXWGXz1MpEntbWBz2ocN5P0siFlXjsf6M+OKZoAoDKv5TBBCSY1qq6LPAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:34:13.634848Z","bundle_sha256":"135d13d4eee8f9c28aa7fb324212014b43c327674a70acdfccf7b74644d4da45"}}