{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Y4WLQLVPRZLCLIZTVPGUY5HN3U","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":"55a8a45c7ed5cefbea155d1bd92cc00db948e33df8e045cc8e1203b293f435f0","cross_cats_sorted":["cs.DS","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2013-01-12T19:00:15Z","title_canon_sha256":"9443e1d77dabfff2b078958203bd8d790daddae3b64fc931690f52fe95011dea"},"schema_version":"1.0","source":{"id":"1301.2707","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2707","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2707v2","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2707","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"Y4WLQLVPRZLC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y4WLQLVPRZLCLIZT","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y4WLQLVP","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:cf0f141d74a481b52fc82dcba4744c1764a9aa6beb02ba6c5c434b1f90a87694","target":"graph","created_at":"2026-05-18T02:20:12Z","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":"We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite preconditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program uni","authors_text":"Michael A. Saunders, Sou-Cheng T. Choi","cross_cats":["cs.DS","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2013-01-12T19:00:15Z","title":"ALGORITHM 937: MINRES-QLP for Singular Symmetric and Hermitian Linear Equations and Least-Squares Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2707","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":"sha256:569f3814e9732acd83b57898671b80af192e1b53feaf14bf037672862ef1e0d6","target":"record","created_at":"2026-05-18T02:20:12Z","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":"55a8a45c7ed5cefbea155d1bd92cc00db948e33df8e045cc8e1203b293f435f0","cross_cats_sorted":["cs.DS","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2013-01-12T19:00:15Z","title_canon_sha256":"9443e1d77dabfff2b078958203bd8d790daddae3b64fc931690f52fe95011dea"},"schema_version":"1.0","source":{"id":"1301.2707","kind":"arxiv","version":2}},"canonical_sha256":"c72cb82eaf8e5625a333abcd4c74eddd194e44122464701443ce9a120e7da574","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c72cb82eaf8e5625a333abcd4c74eddd194e44122464701443ce9a120e7da574","first_computed_at":"2026-05-18T02:20:12.873820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:12.873820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1kXbYFla+HUvd+9Fj3FsM5l4IkGLWlbdCj08lVnsrrRjAhrQhFAmhAxOBJdpZhAVbMsM/IkMhnEofq4Rhu00AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:12.874308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2707","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:569f3814e9732acd83b57898671b80af192e1b53feaf14bf037672862ef1e0d6","sha256:cf0f141d74a481b52fc82dcba4744c1764a9aa6beb02ba6c5c434b1f90a87694"],"state_sha256":"810b582b0f42173425be7cdd69d0aef22c040b96fea43b6703f8ffe5a97960c3"}