{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:NVZ2UCHB7OW533UKAHGFMPNRRD","short_pith_number":"pith:NVZ2UCHB","schema_version":"1.0","canonical_sha256":"6d73aa08e1fbadddee8a01cc563db188f165e72d33bde260a7b86d5801f2d797","source":{"kind":"arxiv","id":"1807.11802","version":3},"attestation_state":"computed","paper":{"title":"Adaptive BEM with optimal convergence rates for the Helmholtz equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexander Haberl, Alex Bespalov, Dirk Praetorius, Timo Betcke","submitted_at":"2018-07-31T13:19:05Z","abstract_excerpt":"We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on any a priori information that the underlying meshes are sufficiently fine. We prove convergence of the error estimator with optimal algebraic rates, independently of the (coarse) initial mesh. As a technical contribution, we prove certain local inverse-type estimates for the boundary integral operators associated with the Helmholtz equation."},"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":"1807.11802","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-31T13:19:05Z","cross_cats_sorted":[],"title_canon_sha256":"8fc64f2971fb81eeed73d10aa6480811b5baf1cab891bd1f579b86a6b4ef547a","abstract_canon_sha256":"9dafa777ae00c43ef14f0b071ee7431f538d4d21e6392355d6d67a603b768863"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:49.061580Z","signature_b64":"dsDSJ5Y2NGAZRhujh5yw1dO8FeZFs9V24g41CX88RcYTDXVPcpaExHMcxLohY547eo9860ifIZCouqn66HHhAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d73aa08e1fbadddee8a01cc563db188f165e72d33bde260a7b86d5801f2d797","last_reissued_at":"2026-05-17T23:50:49.060966Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:49.060966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Adaptive BEM with optimal convergence rates for the Helmholtz equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexander Haberl, Alex Bespalov, Dirk Praetorius, Timo Betcke","submitted_at":"2018-07-31T13:19:05Z","abstract_excerpt":"We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on any a priori information that the underlying meshes are sufficiently fine. We prove convergence of the error estimator with optimal algebraic rates, independently of the (coarse) initial mesh. As a technical contribution, we prove certain local inverse-type estimates for the boundary integral operators associated with the Helmholtz equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11802","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1807.11802","created_at":"2026-05-17T23:50:49.061048+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.11802v3","created_at":"2026-05-17T23:50:49.061048+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11802","created_at":"2026-05-17T23:50:49.061048+00:00"},{"alias_kind":"pith_short_12","alias_value":"NVZ2UCHB7OW5","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"NVZ2UCHB7OW533UK","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"NVZ2UCHB","created_at":"2026-05-18T12:32:40.477152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NVZ2UCHB7OW533UKAHGFMPNRRD","json":"https://pith.science/pith/NVZ2UCHB7OW533UKAHGFMPNRRD.json","graph_json":"https://pith.science/api/pith-number/NVZ2UCHB7OW533UKAHGFMPNRRD/graph.json","events_json":"https://pith.science/api/pith-number/NVZ2UCHB7OW533UKAHGFMPNRRD/events.json","paper":"https://pith.science/paper/NVZ2UCHB"},"agent_actions":{"view_html":"https://pith.science/pith/NVZ2UCHB7OW533UKAHGFMPNRRD","download_json":"https://pith.science/pith/NVZ2UCHB7OW533UKAHGFMPNRRD.json","view_paper":"https://pith.science/paper/NVZ2UCHB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.11802&json=true","fetch_graph":"https://pith.science/api/pith-number/NVZ2UCHB7OW533UKAHGFMPNRRD/graph.json","fetch_events":"https://pith.science/api/pith-number/NVZ2UCHB7OW533UKAHGFMPNRRD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NVZ2UCHB7OW533UKAHGFMPNRRD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NVZ2UCHB7OW533UKAHGFMPNRRD/action/storage_attestation","attest_author":"https://pith.science/pith/NVZ2UCHB7OW533UKAHGFMPNRRD/action/author_attestation","sign_citation":"https://pith.science/pith/NVZ2UCHB7OW533UKAHGFMPNRRD/action/citation_signature","submit_replication":"https://pith.science/pith/NVZ2UCHB7OW533UKAHGFMPNRRD/action/replication_record"}},"created_at":"2026-05-17T23:50:49.061048+00:00","updated_at":"2026-05-17T23:50:49.061048+00:00"}