{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:S325VTKXRO2FLO3NCN4JJE7VPZ","short_pith_number":"pith:S325VTKX","canonical_record":{"source":{"id":"1805.10132","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-24T07:23:13Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"be8c3d15f7dbc9558e2355f829276b5c242b7e1aee012722a75936fdffb8afb6","abstract_canon_sha256":"bc0090c334402d48dfc8c2c49e76bb051665ceced313284e1cec55bb11b8d690"},"schema_version":"1.0"},"canonical_sha256":"96f5dacd578bb455bb6d13789493f57e4f08b302b72a35b7f994799c243fcb01","source":{"kind":"arxiv","id":"1805.10132","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10132","created_at":"2026-06-04T19:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10132v3","created_at":"2026-06-04T19:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10132","created_at":"2026-06-04T19:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"S325VTKXRO2F","created_at":"2026-06-04T19:11:55Z"},{"alias_kind":"pith_short_16","alias_value":"S325VTKXRO2FLO3N","created_at":"2026-06-04T19:11:55Z"},{"alias_kind":"pith_short_8","alias_value":"S325VTKX","created_at":"2026-06-04T19:11:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:S325VTKXRO2FLO3NCN4JJE7VPZ","target":"record","payload":{"canonical_record":{"source":{"id":"1805.10132","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-24T07:23:13Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"be8c3d15f7dbc9558e2355f829276b5c242b7e1aee012722a75936fdffb8afb6","abstract_canon_sha256":"bc0090c334402d48dfc8c2c49e76bb051665ceced313284e1cec55bb11b8d690"},"schema_version":"1.0"},"canonical_sha256":"96f5dacd578bb455bb6d13789493f57e4f08b302b72a35b7f994799c243fcb01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:11:55.613689Z","signature_b64":"23/zrm4sSMsmH+OMoeM2P3FmEwp7/QUcKUgw/nhsD8HyN3kyHRTRCcRBDkC75hI8Fd2wWT0x4IfuWGfCbL0zAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96f5dacd578bb455bb6d13789493f57e4f08b302b72a35b7f994799c243fcb01","last_reissued_at":"2026-06-04T19:11:55.613253Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:11:55.613253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.10132","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":"2026-06-04T19:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MJqJnb5ZzJPjlbZGQQKGImefM58WUu6L8S2zpes9HUf+10bNl/kc0haNztI5Eqls1uN1nN4LldsfGBSLp/y0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T01:59:54.308058Z"},"content_sha256":"45e880b785b38c701d1769c13822389d5cef745c07c2e6a3322d50d2f84f8791","schema_version":"1.0","event_id":"sha256:45e880b785b38c701d1769c13822389d5cef745c07c2e6a3322d50d2f84f8791"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:S325VTKXRO2FLO3NCN4JJE7VPZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation Accuracy of the Krylov Subspaces for Linear Discrete Ill-Posed Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Zhongxiao Jia","submitted_at":"2018-05-24T07:23:13Z","abstract_excerpt":"For the large-scale linear discrete ill-posed problem $\\min\\|Ax-b\\|$ or $Ax=b$ with $b$ contaminated by Gaussian white noise, the Lanczos bidiagonalization based Krylov solver LSQR and its mathematically equivalent CGLS, the Conjugate Gradient (CG) method implicitly applied to $A^TAx=A^Tb$, are most commonly used, and CGME, the CG method applied to $\\min\\|AA^Ty-b\\|$ or $AA^Ty=b$ with $x=A^Ty$, and LSMR, which is equivalent to the minimal residual (MINRES) method applied to $A^TAx=A^Tb$, have also been choices. These methods exhibit typical semi-convergence feature, and the iteration number $k$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10132","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1805.10132/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-04T19:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"79eS2FtvkFsh0apx298Pw/ftnsuVztnMyg8XuVHPumpCFZNHI/0FlUG81Lz66rwSloZc/c7y2Wc5RUBANpgqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T01:59:54.308473Z"},"content_sha256":"6b12749b6e138f1cac8beb700ac885090a684468c8c1881034e32a86fd69429e","schema_version":"1.0","event_id":"sha256:6b12749b6e138f1cac8beb700ac885090a684468c8c1881034e32a86fd69429e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S325VTKXRO2FLO3NCN4JJE7VPZ/bundle.json","state_url":"https://pith.science/pith/S325VTKXRO2FLO3NCN4JJE7VPZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S325VTKXRO2FLO3NCN4JJE7VPZ/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":"2026-06-21T01:59:54Z","links":{"resolver":"https://pith.science/pith/S325VTKXRO2FLO3NCN4JJE7VPZ","bundle":"https://pith.science/pith/S325VTKXRO2FLO3NCN4JJE7VPZ/bundle.json","state":"https://pith.science/pith/S325VTKXRO2FLO3NCN4JJE7VPZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S325VTKXRO2FLO3NCN4JJE7VPZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:S325VTKXRO2FLO3NCN4JJE7VPZ","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":"bc0090c334402d48dfc8c2c49e76bb051665ceced313284e1cec55bb11b8d690","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-24T07:23:13Z","title_canon_sha256":"be8c3d15f7dbc9558e2355f829276b5c242b7e1aee012722a75936fdffb8afb6"},"schema_version":"1.0","source":{"id":"1805.10132","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10132","created_at":"2026-06-04T19:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10132v3","created_at":"2026-06-04T19:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10132","created_at":"2026-06-04T19:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"S325VTKXRO2F","created_at":"2026-06-04T19:11:55Z"},{"alias_kind":"pith_short_16","alias_value":"S325VTKXRO2FLO3N","created_at":"2026-06-04T19:11:55Z"},{"alias_kind":"pith_short_8","alias_value":"S325VTKX","created_at":"2026-06-04T19:11:55Z"}],"graph_snapshots":[{"event_id":"sha256:6b12749b6e138f1cac8beb700ac885090a684468c8c1881034e32a86fd69429e","target":"graph","created_at":"2026-06-04T19:11:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1805.10132/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For the large-scale linear discrete ill-posed problem $\\min\\|Ax-b\\|$ or $Ax=b$ with $b$ contaminated by Gaussian white noise, the Lanczos bidiagonalization based Krylov solver LSQR and its mathematically equivalent CGLS, the Conjugate Gradient (CG) method implicitly applied to $A^TAx=A^Tb$, are most commonly used, and CGME, the CG method applied to $\\min\\|AA^Ty-b\\|$ or $AA^Ty=b$ with $x=A^Ty$, and LSMR, which is equivalent to the minimal residual (MINRES) method applied to $A^TAx=A^Tb$, have also been choices. These methods exhibit typical semi-convergence feature, and the iteration number $k$","authors_text":"Zhongxiao Jia","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-24T07:23:13Z","title":"Approximation Accuracy of the Krylov Subspaces for Linear Discrete Ill-Posed Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10132","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":"sha256:45e880b785b38c701d1769c13822389d5cef745c07c2e6a3322d50d2f84f8791","target":"record","created_at":"2026-06-04T19:11:55Z","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":"bc0090c334402d48dfc8c2c49e76bb051665ceced313284e1cec55bb11b8d690","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-24T07:23:13Z","title_canon_sha256":"be8c3d15f7dbc9558e2355f829276b5c242b7e1aee012722a75936fdffb8afb6"},"schema_version":"1.0","source":{"id":"1805.10132","kind":"arxiv","version":3}},"canonical_sha256":"96f5dacd578bb455bb6d13789493f57e4f08b302b72a35b7f994799c243fcb01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96f5dacd578bb455bb6d13789493f57e4f08b302b72a35b7f994799c243fcb01","first_computed_at":"2026-06-04T19:11:55.613253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:11:55.613253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"23/zrm4sSMsmH+OMoeM2P3FmEwp7/QUcKUgw/nhsD8HyN3kyHRTRCcRBDkC75hI8Fd2wWT0x4IfuWGfCbL0zAA==","signature_status":"signed_v1","signed_at":"2026-06-04T19:11:55.613689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10132","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45e880b785b38c701d1769c13822389d5cef745c07c2e6a3322d50d2f84f8791","sha256:6b12749b6e138f1cac8beb700ac885090a684468c8c1881034e32a86fd69429e"],"state_sha256":"b8e2532c772147525a2a5f6798657eacbac882d030c3077f8038883a6101dcdc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rg3nN6yaCXfEDCC5ELI1JnK4LUrVBEiqw1ngiEG3dT2DQC16kInWrqOzYLE/tZVLWT+GLoMXs0JH08TfqqCtCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T01:59:54.310865Z","bundle_sha256":"ac4794972852313b93a481d55715dc2a5fe210a8afa015b06d63603b6976f7aa"}}