{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JUIZHDRVFKB4CFG3MT4YBHFCT2","short_pith_number":"pith:JUIZHDRV","canonical_record":{"source":{"id":"1211.4461","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-19T15:23:31Z","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"title_canon_sha256":"0de8ae9f5ae6a12ccfdb8227e9b596428bbf9c4d176f082a1aa7f66333d533bb","abstract_canon_sha256":"48eb6bc9c37ced01483a06f757b07eaaa3fd5da72238d5c729c6d088f0b878c5"},"schema_version":"1.0"},"canonical_sha256":"4d11938e352a83c114db64f9809ca29e85748be68e3fd01b26e740f540bddbbb","source":{"kind":"arxiv","id":"1211.4461","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4461","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4461v5","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4461","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"JUIZHDRVFKB4","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JUIZHDRVFKB4CFG3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JUIZHDRV","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JUIZHDRVFKB4CFG3MT4YBHFCT2","target":"record","payload":{"canonical_record":{"source":{"id":"1211.4461","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-19T15:23:31Z","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"title_canon_sha256":"0de8ae9f5ae6a12ccfdb8227e9b596428bbf9c4d176f082a1aa7f66333d533bb","abstract_canon_sha256":"48eb6bc9c37ced01483a06f757b07eaaa3fd5da72238d5c729c6d088f0b878c5"},"schema_version":"1.0"},"canonical_sha256":"4d11938e352a83c114db64f9809ca29e85748be68e3fd01b26e740f540bddbbb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:24.471332Z","signature_b64":"a9atYtzv3OWaMx3YM/7/NkzJ0rNja2e7grfWhNUJrNWKPcPrdxCsqAm+u+gj+i7iRMStOE/ZPA89slIRCJ/HAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d11938e352a83c114db64f9809ca29e85748be68e3fd01b26e740f540bddbbb","last_reissued_at":"2026-05-18T02:50:24.470908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:24.470908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.4461","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":"2026-05-18T02:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZfVB/XZ8LvvwEKyHOGyBlzIxiIGZHLb8RRB8S1UqWTebgL+3JiOkPYFk5ajS7xUbAUjhLa+96F3uL47QskkcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:03:24.621494Z"},"content_sha256":"5ba604ca16292b1e7056cde33bb36870baaa868dd471cf0b5f1b298032bfdcc8","schema_version":"1.0","event_id":"sha256:5ba604ca16292b1e7056cde33bb36870baaa868dd471cf0b5f1b298032bfdcc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JUIZHDRVFKB4CFG3MT4YBHFCT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An efficient multigrid calculation of the far field map for Helmholtz and Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP"],"primary_cat":"math.NA","authors_text":"Bram Reps, Siegfried Cools, Wim Vanroose","submitted_at":"2012-11-19T15:23:31Z","abstract_excerpt":"In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by extension, Schr\\\"odinger's equation. The new technique is based upon a reformulation of the classical real-valued Green's function integral for the far field amplitude to an equivalent integral over a complex domain. It is shown that the scattered wave, which is essential for the calculation of the far field integral, can be computed very efficiently along this complex contour (or manifold, in multip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4461","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":"2026-05-18T02:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IAW0otggVQyZ67E3Qia8RLYZ+CURiQ/vP+TvOzwIfMaEYMDdejhFAOJ1bnUDCZ9wfWFPbj7JAC/IVpmVMSooAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:03:24.622122Z"},"content_sha256":"7e8cc8403bee82cf288f7cb2d585673e0ea2387804a687fc49cfbae9afea17f8","schema_version":"1.0","event_id":"sha256:7e8cc8403bee82cf288f7cb2d585673e0ea2387804a687fc49cfbae9afea17f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JUIZHDRVFKB4CFG3MT4YBHFCT2/bundle.json","state_url":"https://pith.science/pith/JUIZHDRVFKB4CFG3MT4YBHFCT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JUIZHDRVFKB4CFG3MT4YBHFCT2/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":"2026-05-26T19:03:24Z","links":{"resolver":"https://pith.science/pith/JUIZHDRVFKB4CFG3MT4YBHFCT2","bundle":"https://pith.science/pith/JUIZHDRVFKB4CFG3MT4YBHFCT2/bundle.json","state":"https://pith.science/pith/JUIZHDRVFKB4CFG3MT4YBHFCT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JUIZHDRVFKB4CFG3MT4YBHFCT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JUIZHDRVFKB4CFG3MT4YBHFCT2","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":"48eb6bc9c37ced01483a06f757b07eaaa3fd5da72238d5c729c6d088f0b878c5","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-19T15:23:31Z","title_canon_sha256":"0de8ae9f5ae6a12ccfdb8227e9b596428bbf9c4d176f082a1aa7f66333d533bb"},"schema_version":"1.0","source":{"id":"1211.4461","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4461","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4461v5","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4461","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"JUIZHDRVFKB4","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JUIZHDRVFKB4CFG3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JUIZHDRV","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:7e8cc8403bee82cf288f7cb2d585673e0ea2387804a687fc49cfbae9afea17f8","target":"graph","created_at":"2026-05-18T02:50:24Z","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":"In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by extension, Schr\\\"odinger's equation. The new technique is based upon a reformulation of the classical real-valued Green's function integral for the far field amplitude to an equivalent integral over a complex domain. It is shown that the scattered wave, which is essential for the calculation of the far field integral, can be computed very efficiently along this complex contour (or manifold, in multip","authors_text":"Bram Reps, Siegfried Cools, Wim Vanroose","cross_cats":["cs.NA","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-19T15:23:31Z","title":"An efficient multigrid calculation of the far field map for Helmholtz and Schr\\\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4461","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":"sha256:5ba604ca16292b1e7056cde33bb36870baaa868dd471cf0b5f1b298032bfdcc8","target":"record","created_at":"2026-05-18T02:50:24Z","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":"48eb6bc9c37ced01483a06f757b07eaaa3fd5da72238d5c729c6d088f0b878c5","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-19T15:23:31Z","title_canon_sha256":"0de8ae9f5ae6a12ccfdb8227e9b596428bbf9c4d176f082a1aa7f66333d533bb"},"schema_version":"1.0","source":{"id":"1211.4461","kind":"arxiv","version":5}},"canonical_sha256":"4d11938e352a83c114db64f9809ca29e85748be68e3fd01b26e740f540bddbbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d11938e352a83c114db64f9809ca29e85748be68e3fd01b26e740f540bddbbb","first_computed_at":"2026-05-18T02:50:24.470908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:24.470908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a9atYtzv3OWaMx3YM/7/NkzJ0rNja2e7grfWhNUJrNWKPcPrdxCsqAm+u+gj+i7iRMStOE/ZPA89slIRCJ/HAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:24.471332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4461","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ba604ca16292b1e7056cde33bb36870baaa868dd471cf0b5f1b298032bfdcc8","sha256:7e8cc8403bee82cf288f7cb2d585673e0ea2387804a687fc49cfbae9afea17f8"],"state_sha256":"0412cf7b47b1c87384a4bd52b392489bd285189b781b0bdc443a556f0f532694"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+LKmcRRneEOBJ3cY1prbLEPxi5zaYej2Kz1Vr49QUfcoJ/Y4hrdeUkxnA1mYgGAsraJhqjJUqME/VENQEu3LBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:03:24.625734Z","bundle_sha256":"e518848ecdf0312ae97b1fa6a9d1a51c9b7d4b28bdac32bbd656edd58057b7ba"}}