{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DH2KLMM3YVKHEIDW4AIPTCWZFI","short_pith_number":"pith:DH2KLMM3","canonical_record":{"source":{"id":"1412.2024","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T15:14:05Z","cross_cats_sorted":[],"title_canon_sha256":"5f03b99523cf7412226867d00fb79d36d840696e835f2d9ca975bca2d0c89a2f","abstract_canon_sha256":"65cb0c3a7ab18fbddffb26b41d3b22ff951de3051a510efa9b6a973f79401dbd"},"schema_version":"1.0"},"canonical_sha256":"19f4a5b19bc554722076e010f98ad92a30e477e79dcdd877534ff52d4518a10a","source":{"kind":"arxiv","id":"1412.2024","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2024","created_at":"2026-05-18T01:32:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2024v2","created_at":"2026-05-18T01:32:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2024","created_at":"2026-05-18T01:32:30Z"},{"alias_kind":"pith_short_12","alias_value":"DH2KLMM3YVKH","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DH2KLMM3YVKHEIDW","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DH2KLMM3","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DH2KLMM3YVKHEIDW4AIPTCWZFI","target":"record","payload":{"canonical_record":{"source":{"id":"1412.2024","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T15:14:05Z","cross_cats_sorted":[],"title_canon_sha256":"5f03b99523cf7412226867d00fb79d36d840696e835f2d9ca975bca2d0c89a2f","abstract_canon_sha256":"65cb0c3a7ab18fbddffb26b41d3b22ff951de3051a510efa9b6a973f79401dbd"},"schema_version":"1.0"},"canonical_sha256":"19f4a5b19bc554722076e010f98ad92a30e477e79dcdd877534ff52d4518a10a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:30.491247Z","signature_b64":"5+ujRmsu5BH0aTl40OzDlpAOraMMaUWNAXaaBexRwA82ywWE5xrGknzGkgaG0wAcfUjQ4OKJHXP39/AMdVIMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19f4a5b19bc554722076e010f98ad92a30e477e79dcdd877534ff52d4518a10a","last_reissued_at":"2026-05-18T01:32:30.490746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:30.490746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.2024","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kdWUra+THBaPoT4FlCanxBNACwA4kX1OARnaVuUyleqhIyNQxZOL+IoBISyYrjVJW47GtT1CIV3Uf/fSJXu+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:03:47.309373Z"},"content_sha256":"66ff254ae441f210a4f2920e5a7e4062f92907a83542ea8ef1cfc68b8c348259","schema_version":"1.0","event_id":"sha256:66ff254ae441f210a4f2920e5a7e4062f92907a83542ea8ef1cfc68b8c348259"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DH2KLMM3YVKHEIDW4AIPTCWZFI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal additive Schwarz methods for the $hp$-BEM: the hypersingular integral operator in 3D on locally refined meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexander Rieder, Dirk Praetorius, Jens Markus Melenk, Thomas F\\\"uhrer","submitted_at":"2014-12-05T15:14:05Z","abstract_excerpt":"We propose and analyze an overlapping Schwarz preconditioner for the $p$ and $hp$ boundary element method for the hypersingular integral equation in 3D. We consider surface triangulations consisting of triangles. The condition number is bounded uniformly in the mesh size $h$ and the polynomial order $p$. The preconditioner handles adaptively refined meshes and is based on a local multilevel preconditioner for the lowest order space. Numerical experiments on different geometries illustrate its robustness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2024","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":""},"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":"2026-05-18T01:32:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zKrK5ASSRNDbwaujyng3SYGv8DMKFJrQ/orpNhkJmGzpiY06LhocetJQ6N/m6xCYyc8o71vzmWliEcoEsD6bBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:03:47.310038Z"},"content_sha256":"8a49b34877710cacb9759de96eb364e6ba79f530ac7eaf503b893fc2aebbf35d","schema_version":"1.0","event_id":"sha256:8a49b34877710cacb9759de96eb364e6ba79f530ac7eaf503b893fc2aebbf35d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DH2KLMM3YVKHEIDW4AIPTCWZFI/bundle.json","state_url":"https://pith.science/pith/DH2KLMM3YVKHEIDW4AIPTCWZFI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DH2KLMM3YVKHEIDW4AIPTCWZFI/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":"2026-05-20T05:03:47Z","links":{"resolver":"https://pith.science/pith/DH2KLMM3YVKHEIDW4AIPTCWZFI","bundle":"https://pith.science/pith/DH2KLMM3YVKHEIDW4AIPTCWZFI/bundle.json","state":"https://pith.science/pith/DH2KLMM3YVKHEIDW4AIPTCWZFI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DH2KLMM3YVKHEIDW4AIPTCWZFI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DH2KLMM3YVKHEIDW4AIPTCWZFI","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":"65cb0c3a7ab18fbddffb26b41d3b22ff951de3051a510efa9b6a973f79401dbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T15:14:05Z","title_canon_sha256":"5f03b99523cf7412226867d00fb79d36d840696e835f2d9ca975bca2d0c89a2f"},"schema_version":"1.0","source":{"id":"1412.2024","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2024","created_at":"2026-05-18T01:32:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2024v2","created_at":"2026-05-18T01:32:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2024","created_at":"2026-05-18T01:32:30Z"},{"alias_kind":"pith_short_12","alias_value":"DH2KLMM3YVKH","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DH2KLMM3YVKHEIDW","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DH2KLMM3","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:8a49b34877710cacb9759de96eb364e6ba79f530ac7eaf503b893fc2aebbf35d","target":"graph","created_at":"2026-05-18T01:32:30Z","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 propose and analyze an overlapping Schwarz preconditioner for the $p$ and $hp$ boundary element method for the hypersingular integral equation in 3D. We consider surface triangulations consisting of triangles. The condition number is bounded uniformly in the mesh size $h$ and the polynomial order $p$. The preconditioner handles adaptively refined meshes and is based on a local multilevel preconditioner for the lowest order space. Numerical experiments on different geometries illustrate its robustness.","authors_text":"Alexander Rieder, Dirk Praetorius, Jens Markus Melenk, Thomas F\\\"uhrer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T15:14:05Z","title":"Optimal additive Schwarz methods for the $hp$-BEM: the hypersingular integral operator in 3D on locally refined meshes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2024","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":"sha256:66ff254ae441f210a4f2920e5a7e4062f92907a83542ea8ef1cfc68b8c348259","target":"record","created_at":"2026-05-18T01:32:30Z","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":"65cb0c3a7ab18fbddffb26b41d3b22ff951de3051a510efa9b6a973f79401dbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-05T15:14:05Z","title_canon_sha256":"5f03b99523cf7412226867d00fb79d36d840696e835f2d9ca975bca2d0c89a2f"},"schema_version":"1.0","source":{"id":"1412.2024","kind":"arxiv","version":2}},"canonical_sha256":"19f4a5b19bc554722076e010f98ad92a30e477e79dcdd877534ff52d4518a10a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19f4a5b19bc554722076e010f98ad92a30e477e79dcdd877534ff52d4518a10a","first_computed_at":"2026-05-18T01:32:30.490746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:30.490746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5+ujRmsu5BH0aTl40OzDlpAOraMMaUWNAXaaBexRwA82ywWE5xrGknzGkgaG0wAcfUjQ4OKJHXP39/AMdVIMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:30.491247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2024","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66ff254ae441f210a4f2920e5a7e4062f92907a83542ea8ef1cfc68b8c348259","sha256:8a49b34877710cacb9759de96eb364e6ba79f530ac7eaf503b893fc2aebbf35d"],"state_sha256":"a8625b14fbb0c90fe48a426b1d3a0d217b250c59fb4f6be596f7bac43e34b6cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XE1x2s7/hqqFASJS+vX+HfGCY3otXn+Fo+prMoJ+UsoHvPGs1lCI+LH/ibMfXdMIrE0q4jr5tdnCyPGrOMnGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T05:03:47.314128Z","bundle_sha256":"bbb696c9467c9c3921705ac9be4fffa792a11d6c4911a5bbaa28e224e1f336c4"}}