{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TEZQPCDEJ66DMLMHXOGDLQ3DV2","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":"2b7366ed45fe1c3a1266b21bae2a8093d37a8ae1cd45b86f8fee8ac2086cbfc2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-15T12:48:12Z","title_canon_sha256":"2552cbb8da8d8a437477f30e45793ef8d5e9b0f8b9c28877f4abd7c6cf976335"},"schema_version":"1.0","source":{"id":"1806.05934","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05934","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05934v2","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05934","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"TEZQPCDEJ66D","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"pith_short_16","alias_value":"TEZQPCDEJ66DMLMH","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"pith_short_8","alias_value":"TEZQPCDE","created_at":"2026-06-04T19:11:58Z"}],"graph_snapshots":[{"event_id":"sha256:ba8009fd98a22ba1fc8e80a939bbff4b968a72d38401a7573d1ccb70b05ff800","target":"graph","created_at":"2026-06-04T19:11:58Z","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/1806.05934/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A new, coercive formulation of the Helmholtz equation was introduced in [Moiola, Spence, SIAM Rev. 2014]. In this paper we investigate $h$-version Galerkin discretisations of this formulation, and the iterative solution of the resulting linear systems. We find that the coercive formulation behaves similarly to the standard formulation in terms of the pollution effect (i.e. to maintain accuracy as $k\\to\\infty$, $h$ must decrease with $k$ at the same rate as for the standard formulation). We prove $k$-explicit bounds on the number of GMRES iterations required to solve the linear system of the ne","authors_text":"Andrea Moiola, Euan A. Spence, Ganesh C. Diwan","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-15T12:48:12Z","title":"Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05934","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":"sha256:23887addc2c115a7641983da3fd550efdb37f714553b3fdb228b2506910b5bcc","target":"record","created_at":"2026-06-04T19:11:58Z","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":"2b7366ed45fe1c3a1266b21bae2a8093d37a8ae1cd45b86f8fee8ac2086cbfc2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-15T12:48:12Z","title_canon_sha256":"2552cbb8da8d8a437477f30e45793ef8d5e9b0f8b9c28877f4abd7c6cf976335"},"schema_version":"1.0","source":{"id":"1806.05934","kind":"arxiv","version":2}},"canonical_sha256":"99330788644fbc362d87bb8c35c363aeadc03832d95129f6ef5a64e5e10d6a34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99330788644fbc362d87bb8c35c363aeadc03832d95129f6ef5a64e5e10d6a34","first_computed_at":"2026-06-04T19:11:58.974254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:11:58.974254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nRcCVCNS8gdjHP1q0N9CEryqEECjSRgUXOsr0B6PInMt/5hqXpZO/QlISbrr3YsmR1GtUL1IXxashIi7dMJRBw==","signature_status":"signed_v1","signed_at":"2026-06-04T19:11:58.974739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05934","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23887addc2c115a7641983da3fd550efdb37f714553b3fdb228b2506910b5bcc","sha256:ba8009fd98a22ba1fc8e80a939bbff4b968a72d38401a7573d1ccb70b05ff800"],"state_sha256":"5b4a767a8a4f99db421bfac351177659352c2ef5422fdd23903fc6e97c95b513"}