{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OZ2IQB6JWJOOWOYLECQXLVPTZY","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":"fce791e5bf316a92ae5927147c3d9848163a537bcf52a41c15cbc23dcccffcbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-06T08:19:16Z","title_canon_sha256":"4f60bc7875c02fa7b48cead73de380981b9f0484928fec5eb9d75aa94a9dc49d"},"schema_version":"1.0","source":{"id":"1710.02307","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02307","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02307v2","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02307","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"OZ2IQB6JWJOO","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OZ2IQB6JWJOOWOYL","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OZ2IQB6J","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:1e5f5b489564c8fe8aec44d43e3d2d319a30d44caad19d73f0902f57bc3dc561","target":"graph","created_at":"2026-05-18T00:11:40Z","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 a hybrid approach to solve the high-frequency Helmholtz equation with point source terms in smooth heterogeneous media. The method is based on the ray-based finite element method (ray-FEM), whose original version can not handle the singularity close to point sources accurately. This pitfall is addressed by combining the ray-FEM, which is used to compute the smooth far-field of the solution accurately, with a high-order asymptotic expansion close to the point source, which is used to properly capture the singularity of the solution in the near-field. The method requires a fixed numbe","authors_text":"Hongkai Zhao, Jianliang Qian, Jun Fang, Leonardo Zepeda-N\\'u\\~nez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-06T08:19:16Z","title":"A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02307","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":"sha256:0de0499622cb67b9791e8c908624240dad5e070e3ab73cc134aad2c29d3ab2ad","target":"record","created_at":"2026-05-18T00:11:40Z","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":"fce791e5bf316a92ae5927147c3d9848163a537bcf52a41c15cbc23dcccffcbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-06T08:19:16Z","title_canon_sha256":"4f60bc7875c02fa7b48cead73de380981b9f0484928fec5eb9d75aa94a9dc49d"},"schema_version":"1.0","source":{"id":"1710.02307","kind":"arxiv","version":2}},"canonical_sha256":"76748807c9b25ceb3b0b20a175d5f3ce03a625d663ffcaaf7730833df5f40629","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76748807c9b25ceb3b0b20a175d5f3ce03a625d663ffcaaf7730833df5f40629","first_computed_at":"2026-05-18T00:11:40.642511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:40.642511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IZzRQFLb3K3F5h0acH0FLlWfNdufyVkAp81lnL5vIbKmWTrvB630ayZHV4sRJ406u4RToZRYh82ok57gL3A9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:40.643346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.02307","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0de0499622cb67b9791e8c908624240dad5e070e3ab73cc134aad2c29d3ab2ad","sha256:1e5f5b489564c8fe8aec44d43e3d2d319a30d44caad19d73f0902f57bc3dc561"],"state_sha256":"5345d305b105ef6817265e5c98e1e0aa4ba6ff18a826d2f98dfffb5a114a48aa"}