{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JGGXMSG6VT5OXCPQS2NOHF6QBR","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":"ff670fc24c5e84e00e8da26ad912c4afd9d9f8d527057f31371dcd28ba7faeec","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-12-22T19:08:25Z","title_canon_sha256":"8daed66356769a35ad2ffc1ee03e81a0cb5804cedb38c11c9b1fad583372bd28"},"schema_version":"1.0","source":{"id":"2312.15022","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.15022","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"arxiv_version","alias_value":"2312.15022v2","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.15022","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"pith_short_12","alias_value":"JGGXMSG6VT5O","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"pith_short_16","alias_value":"JGGXMSG6VT5OXCPQ","created_at":"2026-07-05T10:18:07Z"},{"alias_kind":"pith_short_8","alias_value":"JGGXMSG6","created_at":"2026-07-05T10:18:07Z"}],"graph_snapshots":[{"event_id":"sha256:adf9301c2427ad28a36266b8207eb9982b4939e86f7baafae00020bebccada8a","target":"graph","created_at":"2026-07-05T10:18:07Z","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/2312.15022/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"If the numerical range of a matrix is contained in the right half of the complex plane, the GMRES algorithm for solving linear systems will reduce the norm of the residual at every iteration. In his Ph.D. dissertation, Howard Elman derived a bound that guarantees convergence. When the numerical range contains the origin, GMRES need not make progress at every step and Elman's bound does not apply, even if all the eigenvalues are located in the right half-plane. However by solving a Lyapunov equation, one can construct an inner product in which the numerical range is contained in the right half-","authors_text":"Mark Embree","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-12-22T19:08:25Z","title":"Extending Elman's Bound for GMRES"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.15022","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:b0f4e04a534b523e2b116a9a423a781fe44f001554900906182f00d9591fd423","target":"record","created_at":"2026-07-05T10:18:07Z","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":"ff670fc24c5e84e00e8da26ad912c4afd9d9f8d527057f31371dcd28ba7faeec","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-12-22T19:08:25Z","title_canon_sha256":"8daed66356769a35ad2ffc1ee03e81a0cb5804cedb38c11c9b1fad583372bd28"},"schema_version":"1.0","source":{"id":"2312.15022","kind":"arxiv","version":2}},"canonical_sha256":"498d7648deacfaeb89f0969ae397d00c6fdcab1191fae15b289f04e492716e6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"498d7648deacfaeb89f0969ae397d00c6fdcab1191fae15b289f04e492716e6c","first_computed_at":"2026-07-05T10:18:07.302965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:18:07.302965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bpra6G8N7aK+ozG0frOAUqatj1PemCYugkYkekB8XmX8RR77qD2dY/99rZrKYoGi/jaZg2p8iDg/o3301rtDBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:18:07.303611Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.15022","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0f4e04a534b523e2b116a9a423a781fe44f001554900906182f00d9591fd423","sha256:adf9301c2427ad28a36266b8207eb9982b4939e86f7baafae00020bebccada8a"],"state_sha256":"b7f42dfacea8494df791d676fcdf0ab1a0432d90acf9d490f8c5f0eeabb018f4"}