{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:K72CSE33ZLZYPGTK6YN5JCBXZG","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":"48d587c5a6318f9e9fef6b1fb4fc6c61f608a829720cdf48b1b2f1aebf3938f2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-21T20:24:31Z","title_canon_sha256":"495886e86be1ac664e2a3bcdc0f706bfb5424e24cc7b65a44c2506d317870093"},"schema_version":"1.0","source":{"id":"1902.08250","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08250","created_at":"2026-06-04T20:13:55Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08250v1","created_at":"2026-06-04T20:13:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08250","created_at":"2026-06-04T20:13:55Z"},{"alias_kind":"pith_short_12","alias_value":"K72CSE33ZLZY","created_at":"2026-06-04T20:13:55Z"},{"alias_kind":"pith_short_16","alias_value":"K72CSE33ZLZYPGTK","created_at":"2026-06-04T20:13:55Z"},{"alias_kind":"pith_short_8","alias_value":"K72CSE33","created_at":"2026-06-04T20:13:55Z"}],"graph_snapshots":[{"event_id":"sha256:88d357aa951a7e28f9d789d402c5403f08d15cacf795fe4d999ea9dd596f7b0f","target":"graph","created_at":"2026-06-04T20:13:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1902.08250/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present a numerical algorithm for the accurate and efficient computation of the convolution of the frequency domain layered media Green's function with a given density function. Instead of compressing the convolution matrix directly as in the classical fast multipole method, fast direct solvers, and fast H-matrix algorithms, the new algorithm considers a translated form of the original matrix so that many existing building blocks from the highly optimized free-space fast multipole method can be easily adapted to the Sommerfeld integral representations of the layered media Gre","authors_text":"Jingfang Huang, Min Hyung Cho","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-21T20:24:31Z","title":"Adapting free-space fast multipole method for layered media Green's function: algorithm and analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08250","kind":"arxiv","version":1},"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":"sha256:75419dffdb8efdc7d9260e61bcf50002cb41e28dea0a39c06fbfe04b1c449c8f","target":"record","created_at":"2026-06-04T20:13:55Z","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":"48d587c5a6318f9e9fef6b1fb4fc6c61f608a829720cdf48b1b2f1aebf3938f2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-21T20:24:31Z","title_canon_sha256":"495886e86be1ac664e2a3bcdc0f706bfb5424e24cc7b65a44c2506d317870093"},"schema_version":"1.0","source":{"id":"1902.08250","kind":"arxiv","version":1}},"canonical_sha256":"57f429137bcaf3879a6af61bd48837c9af5d53544b0e063d8ed6e6c1a03e56bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57f429137bcaf3879a6af61bd48837c9af5d53544b0e063d8ed6e6c1a03e56bf","first_computed_at":"2026-06-04T20:13:55.404426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T20:13:55.404426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j8YFKnV4J3W7/i9pmuEviSIqScHKQ8LybrGlW/WdaUdE7SQ3drSAC3dXLS1R2FhQoOmbFGzbuBr3IKzQySSBBg==","signature_status":"signed_v1","signed_at":"2026-06-04T20:13:55.404884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.08250","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75419dffdb8efdc7d9260e61bcf50002cb41e28dea0a39c06fbfe04b1c449c8f","sha256:88d357aa951a7e28f9d789d402c5403f08d15cacf795fe4d999ea9dd596f7b0f"],"state_sha256":"4553fb328a7e8e749227c6a91a74afa5bd33bb4831e8fe0f268c81d8d623bb73"}