{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2NL7TXCK5CTR2HSC3BLAGQU3MB","short_pith_number":"pith:2NL7TXCK","canonical_record":{"source":{"id":"1608.01035","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-03T00:23:37Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"41e0d20c77ae67923be21f74de5468a62adcc004594627d89b4b1a8efa422847","abstract_canon_sha256":"44ac6910c1733e3fdc8b710f8dafb3452d3ec2f739fa62f7c41187c2083e3cec"},"schema_version":"1.0"},"canonical_sha256":"d357f9dc4ae8a71d1e42d85603429b6079bb546922bb7989aa3bb985c4f026a8","source":{"kind":"arxiv","id":"1608.01035","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01035","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01035v5","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01035","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"pith_short_12","alias_value":"2NL7TXCK5CTR","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2NL7TXCK5CTR2HSC","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2NL7TXCK","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2NL7TXCK5CTR2HSC3BLAGQU3MB","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01035","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-03T00:23:37Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"41e0d20c77ae67923be21f74de5468a62adcc004594627d89b4b1a8efa422847","abstract_canon_sha256":"44ac6910c1733e3fdc8b710f8dafb3452d3ec2f739fa62f7c41187c2083e3cec"},"schema_version":"1.0"},"canonical_sha256":"d357f9dc4ae8a71d1e42d85603429b6079bb546922bb7989aa3bb985c4f026a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:01.629629Z","signature_b64":"w+SPvj3WvEuH0ZgNZ1UbMlzExnFM+GdWLzEDPH1E+Mx9NIhFw2n1bcI3P3F6H0Xp4sE7zXSW1WbIg/B2FMVqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d357f9dc4ae8a71d1e42d85603429b6079bb546922bb7989aa3bb985c4f026a8","last_reissued_at":"2026-05-17T23:53:01.629038Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:01.629038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01035","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KFf7w2yDfo4XWc1fjKh2eDQPlp1eAtsLVGCR7uvFMz+3Qy+K+HM/RDFwjkdk56r3WEuywXVv9lymWszJU5FbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:45:12.569635Z"},"content_sha256":"9a11ce13c0509abe73e9c1cff25619161673056e349824dad23a0fd047f0f294","schema_version":"1.0","event_id":"sha256:9a11ce13c0509abe73e9c1cff25619161673056e349824dad23a0fd047f0f294"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2NL7TXCK5CTR2HSC3BLAGQU3MB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wavenumber-explicit analysis for the Helmholtz $h$-BEM: error estimates and iteration counts for the Dirichlet problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Eike H. M\\\"uller, Euan A. Spence, Jeffrey Galkowski","submitted_at":"2016-08-03T00:23:37Z","abstract_excerpt":"We consider solving the exterior Dirichlet problem for the Helmholtz equation with the $h$-version of the boundary element method (BEM) using the standard second-kind combined-field integral equations. We prove a new, sharp bound on how the number of GMRES iterations must grow with the wavenumber $k$ to have the error in the iterative solution bounded independently of $k$ as $k\\rightarrow \\infty$ when the boundary of the obstacle is analytic and has strictly positive curvature. To our knowledge, this result is the first-ever sharp bound on how the number of GMRES iterations depends on the wave"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01035","kind":"arxiv","version":5},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H6PKw8ZiR6GGbNN427O65HDP6Q6VJybB41NyM+/Hw2kJawJOB0h6XZWpo1ctWL/i0m4F5DiZr2Y52HmD5NAhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:45:12.569983Z"},"content_sha256":"7b2a3c74c0ce71718d330fd4ba66d544b500f5f655b5c767966e8fe5776d66bb","schema_version":"1.0","event_id":"sha256:7b2a3c74c0ce71718d330fd4ba66d544b500f5f655b5c767966e8fe5776d66bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2NL7TXCK5CTR2HSC3BLAGQU3MB/bundle.json","state_url":"https://pith.science/pith/2NL7TXCK5CTR2HSC3BLAGQU3MB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2NL7TXCK5CTR2HSC3BLAGQU3MB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T19:45:12Z","links":{"resolver":"https://pith.science/pith/2NL7TXCK5CTR2HSC3BLAGQU3MB","bundle":"https://pith.science/pith/2NL7TXCK5CTR2HSC3BLAGQU3MB/bundle.json","state":"https://pith.science/pith/2NL7TXCK5CTR2HSC3BLAGQU3MB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2NL7TXCK5CTR2HSC3BLAGQU3MB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2NL7TXCK5CTR2HSC3BLAGQU3MB","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":"44ac6910c1733e3fdc8b710f8dafb3452d3ec2f739fa62f7c41187c2083e3cec","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-03T00:23:37Z","title_canon_sha256":"41e0d20c77ae67923be21f74de5468a62adcc004594627d89b4b1a8efa422847"},"schema_version":"1.0","source":{"id":"1608.01035","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01035","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01035v5","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01035","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"pith_short_12","alias_value":"2NL7TXCK5CTR","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2NL7TXCK5CTR2HSC","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2NL7TXCK","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:7b2a3c74c0ce71718d330fd4ba66d544b500f5f655b5c767966e8fe5776d66bb","target":"graph","created_at":"2026-05-17T23:53:01Z","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"},"paper":{"abstract_excerpt":"We consider solving the exterior Dirichlet problem for the Helmholtz equation with the $h$-version of the boundary element method (BEM) using the standard second-kind combined-field integral equations. We prove a new, sharp bound on how the number of GMRES iterations must grow with the wavenumber $k$ to have the error in the iterative solution bounded independently of $k$ as $k\\rightarrow \\infty$ when the boundary of the obstacle is analytic and has strictly positive curvature. To our knowledge, this result is the first-ever sharp bound on how the number of GMRES iterations depends on the wave","authors_text":"Eike H. M\\\"uller, Euan A. Spence, Jeffrey Galkowski","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-03T00:23:37Z","title":"Wavenumber-explicit analysis for the Helmholtz $h$-BEM: error estimates and iteration counts for the Dirichlet problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01035","kind":"arxiv","version":5},"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":"sha256:9a11ce13c0509abe73e9c1cff25619161673056e349824dad23a0fd047f0f294","target":"record","created_at":"2026-05-17T23:53:01Z","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":"44ac6910c1733e3fdc8b710f8dafb3452d3ec2f739fa62f7c41187c2083e3cec","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-03T00:23:37Z","title_canon_sha256":"41e0d20c77ae67923be21f74de5468a62adcc004594627d89b4b1a8efa422847"},"schema_version":"1.0","source":{"id":"1608.01035","kind":"arxiv","version":5}},"canonical_sha256":"d357f9dc4ae8a71d1e42d85603429b6079bb546922bb7989aa3bb985c4f026a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d357f9dc4ae8a71d1e42d85603429b6079bb546922bb7989aa3bb985c4f026a8","first_computed_at":"2026-05-17T23:53:01.629038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:01.629038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w+SPvj3WvEuH0ZgNZ1UbMlzExnFM+GdWLzEDPH1E+Mx9NIhFw2n1bcI3P3F6H0Xp4sE7zXSW1WbIg/B2FMVqDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:01.629629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01035","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a11ce13c0509abe73e9c1cff25619161673056e349824dad23a0fd047f0f294","sha256:7b2a3c74c0ce71718d330fd4ba66d544b500f5f655b5c767966e8fe5776d66bb"],"state_sha256":"fabffee2c43f15fb9bab6063021f91f013267bea2f40c01461e32377f1f603ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HQLWZgFvk/rvNW7T7DP6EHxLJyiSNOezZBy48X0PSm2qwuMzJBRNvRgdhK3KQ9HxEi4Z9DDi99W39IvBJXzaBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:45:12.571964Z","bundle_sha256":"4394e660d5a78af5d4348fa962a9512058f39943e1490cbb9095320cfb4ef515"}}