{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3OM6PR45V6RSOIV47INTSNMIZ4","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":"b21f4e2d7deeeea8b3f44b8ad4b0b72b9048cb9202828372198b8bbd741a901b","cross_cats_sorted":["math-ph","math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-08T18:03:32Z","title_canon_sha256":"0329737049fb15a40b8121c5ce1cf105c6d60122c81efd2151f6341a2659d796"},"schema_version":"1.0","source":{"id":"1408.1932","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1932","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1932v3","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1932","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"3OM6PR45V6RS","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3OM6PR45V6RSOIV4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3OM6PR45","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:c3f24398824a6138f01fd988e3ba1347e141a4445b1044892ebec945fffab24d","target":"graph","created_at":"2026-05-18T01:19:14Z","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 rigorously investigate the truncation method for the Cauchy problem of Helmholtz equations which is widely used to model propagation phenomena in physical applications. The method is a well-known approach to the regularization of several types of ill-posed problems, including the model postulated by Regi\\' nska and Regi\\' nski \\cite{RR06}. Under certain specific assumptions, we examine the ill-posedness of the non-homogeneous problem by exploring the representation of solutions based on Fourier mode. Then the so-called regularized solution is established with respect to a fre","authors_text":"Huy Tuan Nguyen, Mach Nguyet Minh, Thanh Tran, Vo Anh Khoa","cross_cats":["math-ph","math.MP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-08T18:03:32Z","title":"Reconstruction of the electric field of the Helmholtz equation in 3D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1932","kind":"arxiv","version":3},"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:dd2628763ac3636f8a5d4148ed861802a061642222020dddba12e4ac567fa9a1","target":"record","created_at":"2026-05-18T01:19:14Z","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":"b21f4e2d7deeeea8b3f44b8ad4b0b72b9048cb9202828372198b8bbd741a901b","cross_cats_sorted":["math-ph","math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-08T18:03:32Z","title_canon_sha256":"0329737049fb15a40b8121c5ce1cf105c6d60122c81efd2151f6341a2659d796"},"schema_version":"1.0","source":{"id":"1408.1932","kind":"arxiv","version":3}},"canonical_sha256":"db99e7c79dafa32722bcfa1b393588cf1dbc6ecda969ed6a20a7a329b08c46c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db99e7c79dafa32722bcfa1b393588cf1dbc6ecda969ed6a20a7a329b08c46c7","first_computed_at":"2026-05-18T01:19:14.362461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:14.362461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TSTGWy7LjPzPDDPz+88rNbSmRDw+zmh6bRbHze7AFIFvmoMj8QgUgHn0H3uTKFVzNL+/423FzwVOozXA8NJbDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:14.362952Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1932","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd2628763ac3636f8a5d4148ed861802a061642222020dddba12e4ac567fa9a1","sha256:c3f24398824a6138f01fd988e3ba1347e141a4445b1044892ebec945fffab24d"],"state_sha256":"6fa2fc00a28e916579e3943760d86460805b528b6d02d0adebc6e06ce1223a81"}