{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OACVUCQKZ2S5ODABOUHPIHVODD","short_pith_number":"pith:OACVUCQK","canonical_record":{"source":{"id":"1208.3956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-20T09:42:53Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"5edb32d3b8d7b53226a632b20995d3ed0ddab64e8cdc8904c630536fdceed8f0","abstract_canon_sha256":"69781b1d0bb8ccb8045dce68175c999928755c777d5f45df9d02fa327d52aaa6"},"schema_version":"1.0"},"canonical_sha256":"70055a0a0acea5d70c01750ef41eae18ed7207a7abdfa5cc73343309437e347d","source":{"kind":"arxiv","id":"1208.3956","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3956","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3956v2","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3956","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"pith_short_12","alias_value":"OACVUCQKZ2S5","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OACVUCQKZ2S5ODAB","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OACVUCQK","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OACVUCQKZ2S5ODABOUHPIHVODD","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-20T09:42:53Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"5edb32d3b8d7b53226a632b20995d3ed0ddab64e8cdc8904c630536fdceed8f0","abstract_canon_sha256":"69781b1d0bb8ccb8045dce68175c999928755c777d5f45df9d02fa327d52aaa6"},"schema_version":"1.0"},"canonical_sha256":"70055a0a0acea5d70c01750ef41eae18ed7207a7abdfa5cc73343309437e347d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:20.743897Z","signature_b64":"pV5IeZt2HbMq5iT7o1ZMkC4DYJDdUzkL+pENjhutN2h0PTud7gjYAgjpqcfu07uyEwlFgb6ALq2KYPMA2Lz1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70055a0a0acea5d70c01750ef41eae18ed7207a7abdfa5cc73343309437e347d","last_reissued_at":"2026-05-18T03:20:20.743138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:20.743138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3956","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":"2026-05-18T03:20:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQ9fu3M+jsf/+MjGGF6oozIeelWSJfzSb5i0CoB8xk8rr5JB2AwGUHxLZG4L5coQEO9J3ikQg40EUKLhf1EMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:53:11.652606Z"},"content_sha256":"1afb94a01f1d765553e0d4a8e8464c8f2ab2abd3e163e1f3af41a8e969b27a30","schema_version":"1.0","event_id":"sha256:1afb94a01f1d765553e0d4a8e8464c8f2ab2abd3e163e1f3af41a8e969b27a30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OACVUCQKZ2S5ODABOUHPIHVODD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A rapidly converging domain decomposition method for the Helmholtz equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Christiaan C. Stolk","submitted_at":"2012-08-20T09:42:53Z","abstract_excerpt":"A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and outgoing waves at the subdomain interfaces. We focus on a subdivision of the rectangular domain into many thin subdomains along one of the axes, in combination with a certain ordering for solving the subdomain problems and a GMRES outer iteration. When combined with multifrontal methods, the solver has near-linear cost in examples, due to very small iteration"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3956","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":"2026-05-18T03:20:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rrJA0LcZwGxUKfFUySK3x1BM0fgv2CiRWwwq+PBzojpTO3A5X5T9Aj5emPCsqqCbzpC/2qCS71lhaOGoirm0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:53:11.652948Z"},"content_sha256":"2ad0cfd70d23f4e252c7c8938c02e447797dc7fa6cca59b72f33bac2f2d196cc","schema_version":"1.0","event_id":"sha256:2ad0cfd70d23f4e252c7c8938c02e447797dc7fa6cca59b72f33bac2f2d196cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OACVUCQKZ2S5ODABOUHPIHVODD/bundle.json","state_url":"https://pith.science/pith/OACVUCQKZ2S5ODABOUHPIHVODD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OACVUCQKZ2S5ODABOUHPIHVODD/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":"2026-06-24T02:53:11Z","links":{"resolver":"https://pith.science/pith/OACVUCQKZ2S5ODABOUHPIHVODD","bundle":"https://pith.science/pith/OACVUCQKZ2S5ODABOUHPIHVODD/bundle.json","state":"https://pith.science/pith/OACVUCQKZ2S5ODABOUHPIHVODD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OACVUCQKZ2S5ODABOUHPIHVODD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OACVUCQKZ2S5ODABOUHPIHVODD","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":"69781b1d0bb8ccb8045dce68175c999928755c777d5f45df9d02fa327d52aaa6","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-20T09:42:53Z","title_canon_sha256":"5edb32d3b8d7b53226a632b20995d3ed0ddab64e8cdc8904c630536fdceed8f0"},"schema_version":"1.0","source":{"id":"1208.3956","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3956","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3956v2","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3956","created_at":"2026-05-18T03:20:20Z"},{"alias_kind":"pith_short_12","alias_value":"OACVUCQKZ2S5","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OACVUCQKZ2S5ODAB","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OACVUCQK","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:2ad0cfd70d23f4e252c7c8938c02e447797dc7fa6cca59b72f33bac2f2d196cc","target":"graph","created_at":"2026-05-18T03:20:20Z","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":"A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and outgoing waves at the subdomain interfaces. We focus on a subdivision of the rectangular domain into many thin subdomains along one of the axes, in combination with a certain ordering for solving the subdomain problems and a GMRES outer iteration. When combined with multifrontal methods, the solver has near-linear cost in examples, due to very small iteration","authors_text":"Christiaan C. Stolk","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-20T09:42:53Z","title":"A rapidly converging domain decomposition method for the Helmholtz equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3956","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":"sha256:1afb94a01f1d765553e0d4a8e8464c8f2ab2abd3e163e1f3af41a8e969b27a30","target":"record","created_at":"2026-05-18T03:20:20Z","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":"69781b1d0bb8ccb8045dce68175c999928755c777d5f45df9d02fa327d52aaa6","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-20T09:42:53Z","title_canon_sha256":"5edb32d3b8d7b53226a632b20995d3ed0ddab64e8cdc8904c630536fdceed8f0"},"schema_version":"1.0","source":{"id":"1208.3956","kind":"arxiv","version":2}},"canonical_sha256":"70055a0a0acea5d70c01750ef41eae18ed7207a7abdfa5cc73343309437e347d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70055a0a0acea5d70c01750ef41eae18ed7207a7abdfa5cc73343309437e347d","first_computed_at":"2026-05-18T03:20:20.743138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:20.743138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pV5IeZt2HbMq5iT7o1ZMkC4DYJDdUzkL+pENjhutN2h0PTud7gjYAgjpqcfu07uyEwlFgb6ALq2KYPMA2Lz1Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:20.743897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3956","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1afb94a01f1d765553e0d4a8e8464c8f2ab2abd3e163e1f3af41a8e969b27a30","sha256:2ad0cfd70d23f4e252c7c8938c02e447797dc7fa6cca59b72f33bac2f2d196cc"],"state_sha256":"a469deb00228d508928e4359d407e9e7a665e06ed72cbf4741f2b75b88399f8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sjsPQGxwY6VU9lL6k5SMhaMuRSTHFPWruf6yFpyurL+WbzqzwXNPXhoRq5NQrFYARogdXj2TV09NwqZKxvsDBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T02:53:11.654987Z","bundle_sha256":"2d47613b534cb8afeb5ca08a2c6232b7a451d9de9969dd1dafc92140960fb1a0"}}