{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:SRIOS5CTRJQO2HOEISN5IK5XZJ","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":"56df37ab0ca1a65941d1e4e9c130629d447bf83b501b43e29093ffde4471bdf3","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-29T19:00:56Z","title_canon_sha256":"3e7d58e973daf61c945626892c23decec2454e06d620397449f6523b3e5fc9be"},"schema_version":"1.0","source":{"id":"2307.16051","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.16051","created_at":"2026-07-05T06:58:58Z"},{"alias_kind":"arxiv_version","alias_value":"2307.16051v4","created_at":"2026-07-05T06:58:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.16051","created_at":"2026-07-05T06:58:58Z"},{"alias_kind":"pith_short_12","alias_value":"SRIOS5CTRJQO","created_at":"2026-07-05T06:58:58Z"},{"alias_kind":"pith_short_16","alias_value":"SRIOS5CTRJQO2HOE","created_at":"2026-07-05T06:58:58Z"},{"alias_kind":"pith_short_8","alias_value":"SRIOS5CT","created_at":"2026-07-05T06:58:58Z"}],"graph_snapshots":[{"event_id":"sha256:4dc8dfa5c83d14c6414e492f3d174c558df14c1afebae11c869fd7d096e2a45c","target":"graph","created_at":"2026-07-05T06:58:58Z","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/2307.16051/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with iterative refinement with a factorization in half precision. We analyze the method as an inexact Newton method. This analysis shows that, except for very poorly conditioned Jacobians, the number of nonlinear iterations needed is the same that one would get if one stored and factored the Jacobian in double precision. In many ill-conditioned cases one can use the low","authors_text":"C. T. Kelley","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-29T19:00:56Z","title":"Newton's Method in Three Precisions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.16051","kind":"arxiv","version":4},"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:f753e2e5cc65e1f5848f18c6178d95a66f994b566b42017146affc7a79297005","target":"record","created_at":"2026-07-05T06:58:58Z","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":"56df37ab0ca1a65941d1e4e9c130629d447bf83b501b43e29093ffde4471bdf3","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-29T19:00:56Z","title_canon_sha256":"3e7d58e973daf61c945626892c23decec2454e06d620397449f6523b3e5fc9be"},"schema_version":"1.0","source":{"id":"2307.16051","kind":"arxiv","version":4}},"canonical_sha256":"9450e974538a60ed1dc4449bd42bb7ca606d4873745f2bf7abcdeaf099020676","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9450e974538a60ed1dc4449bd42bb7ca606d4873745f2bf7abcdeaf099020676","first_computed_at":"2026-07-05T06:58:58.739486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:58:58.739486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cq/x19zqdwNUMks6uIXcR6KAX6fCjdHcQjgslocZB13gIuFabVrLpfTUu6InHH8aQkPBtlUDG5w+F4IvjwbYDg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:58:58.739965Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.16051","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f753e2e5cc65e1f5848f18c6178d95a66f994b566b42017146affc7a79297005","sha256:4dc8dfa5c83d14c6414e492f3d174c558df14c1afebae11c869fd7d096e2a45c"],"state_sha256":"bd0939db89bc3ec584378e1a1f35744858adf3331fd60bc507500d0326d26693"}