{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:U5U5MWVDXD45MNNAL2XJBNPRRH","short_pith_number":"pith:U5U5MWVD","schema_version":"1.0","canonical_sha256":"a769d65aa3b8f9d635a05eae90b5f189cb4332732a823133712b197b18bb7192","source":{"kind":"arxiv","id":"2511.15287","version":2},"attestation_state":"computed","paper":{"title":"Numerical analysis of the high-frequency Helmholtz equation using semiclassical analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Euan A. Spence, Jeffrey Galkowski","submitted_at":"2025-11-19T09:52:46Z","abstract_excerpt":"We consider the numerical solution of high-frequency scattering problems modeled by the Helmholtz equation with a bounded obstacle. Although the analysis of this problem dates back at least 50 years, over the past decade or so, tools and techniques from $\\textit{semiclassical analysis}$ have provided a new perspective and been used to settle several long-standing open problems in this area. Semiclassical analysis works in phase space (i.e., position and frequency) and describes rigorously the extent to which solutions of high-frequency PDEs are dictated by the properties of the corresponding g"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2511.15287","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-11-19T09:52:46Z","cross_cats_sorted":["cs.NA","math.AP"],"title_canon_sha256":"ca4df2837570157c0e75c45682bed81f87b7f0175f9031a8ddbd8a16c1ccf8e5","abstract_canon_sha256":"f57f23f6def7c00030663407ff1b489c3a570d2f98706b7ba699afc17d3c4665"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T14:15:53.073036Z","signature_b64":"kagRBm1MBWhfGgY8Kwkz4Mtf2sLBM7yHpqXeYyexyfbFW/i2LXcebkPtTt3g3KL/jkX49QWr88yYh5wD4mjyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a769d65aa3b8f9d635a05eae90b5f189cb4332732a823133712b197b18bb7192","last_reissued_at":"2026-06-24T14:15:53.072603Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T14:15:53.072603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical analysis of the high-frequency Helmholtz equation using semiclassical analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Euan A. Spence, Jeffrey Galkowski","submitted_at":"2025-11-19T09:52:46Z","abstract_excerpt":"We consider the numerical solution of high-frequency scattering problems modeled by the Helmholtz equation with a bounded obstacle. Although the analysis of this problem dates back at least 50 years, over the past decade or so, tools and techniques from $\\textit{semiclassical analysis}$ have provided a new perspective and been used to settle several long-standing open problems in this area. Semiclassical analysis works in phase space (i.e., position and frequency) and describes rigorously the extent to which solutions of high-frequency PDEs are dictated by the properties of the corresponding g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.15287","kind":"arxiv","version":2},"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/2511.15287/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2511.15287","created_at":"2026-06-24T14:15:53.072661+00:00"},{"alias_kind":"arxiv_version","alias_value":"2511.15287v2","created_at":"2026-06-24T14:15:53.072661+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.15287","created_at":"2026-06-24T14:15:53.072661+00:00"},{"alias_kind":"pith_short_12","alias_value":"U5U5MWVDXD45","created_at":"2026-06-24T14:15:53.072661+00:00"},{"alias_kind":"pith_short_16","alias_value":"U5U5MWVDXD45MNNA","created_at":"2026-06-24T14:15:53.072661+00:00"},{"alias_kind":"pith_short_8","alias_value":"U5U5MWVD","created_at":"2026-06-24T14:15:53.072661+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.13489","citing_title":"Spectral Filtering of 3D Integral Operators Using Modified Green's Functions","ref_index":280,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U5U5MWVDXD45MNNAL2XJBNPRRH","json":"https://pith.science/pith/U5U5MWVDXD45MNNAL2XJBNPRRH.json","graph_json":"https://pith.science/api/pith-number/U5U5MWVDXD45MNNAL2XJBNPRRH/graph.json","events_json":"https://pith.science/api/pith-number/U5U5MWVDXD45MNNAL2XJBNPRRH/events.json","paper":"https://pith.science/paper/U5U5MWVD"},"agent_actions":{"view_html":"https://pith.science/pith/U5U5MWVDXD45MNNAL2XJBNPRRH","download_json":"https://pith.science/pith/U5U5MWVDXD45MNNAL2XJBNPRRH.json","view_paper":"https://pith.science/paper/U5U5MWVD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2511.15287&json=true","fetch_graph":"https://pith.science/api/pith-number/U5U5MWVDXD45MNNAL2XJBNPRRH/graph.json","fetch_events":"https://pith.science/api/pith-number/U5U5MWVDXD45MNNAL2XJBNPRRH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U5U5MWVDXD45MNNAL2XJBNPRRH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U5U5MWVDXD45MNNAL2XJBNPRRH/action/storage_attestation","attest_author":"https://pith.science/pith/U5U5MWVDXD45MNNAL2XJBNPRRH/action/author_attestation","sign_citation":"https://pith.science/pith/U5U5MWVDXD45MNNAL2XJBNPRRH/action/citation_signature","submit_replication":"https://pith.science/pith/U5U5MWVDXD45MNNAL2XJBNPRRH/action/replication_record"}},"created_at":"2026-06-24T14:15:53.072661+00:00","updated_at":"2026-06-24T14:15:53.072661+00:00"}