{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:HBJVUV2SXMITF7W6YWKX3KYH3T","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":"d7d4a2ea44597819e74a36c93c83428cef5d0db3e8391eda448ac30325c38128","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-06-18T19:52:09Z","title_canon_sha256":"7ca997927ff064009d93bdcfa085ea4b0c819eca5aac54ede3a33acc280f6b14"},"schema_version":"1.0","source":{"id":"2006.10830","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.10830","created_at":"2026-07-05T01:11:25Z"},{"alias_kind":"arxiv_version","alias_value":"2006.10830v1","created_at":"2026-07-05T01:11:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.10830","created_at":"2026-07-05T01:11:25Z"},{"alias_kind":"pith_short_12","alias_value":"HBJVUV2SXMIT","created_at":"2026-07-05T01:11:25Z"},{"alias_kind":"pith_short_16","alias_value":"HBJVUV2SXMITF7W6","created_at":"2026-07-05T01:11:25Z"},{"alias_kind":"pith_short_8","alias_value":"HBJVUV2S","created_at":"2026-07-05T01:11:25Z"}],"graph_snapshots":[{"event_id":"sha256:1dfe8074f870c03041f764ee4f03b2a478e59915fa85ae6d88d9c0e7f300a63a","target":"graph","created_at":"2026-07-05T01:11:25Z","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/2006.10830/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations. For the numerical solution of these coupled integral equations we propose a fast spectral algorithm by transporting these equations onto the unit sphere. We review the differentiability properties of the boundary to far field operator and give a characterization of the adjoint operator of the first Fr\\'echet derivative. Using these results we discuss the im","authors_text":"Fr\\'ed\\'erique Le Lou\\\"er, Thorsten Hohage","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-06-18T19:52:09Z","title":"A spectrally accurate method for the dielectric obstacle scattering problem and applications to the inverse problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.10830","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:c51d507ebb4e5dec371daf911b470cc7ea799aff50b197dbab2964ca1419dcae","target":"record","created_at":"2026-07-05T01:11:25Z","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":"d7d4a2ea44597819e74a36c93c83428cef5d0db3e8391eda448ac30325c38128","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-06-18T19:52:09Z","title_canon_sha256":"7ca997927ff064009d93bdcfa085ea4b0c819eca5aac54ede3a33acc280f6b14"},"schema_version":"1.0","source":{"id":"2006.10830","kind":"arxiv","version":1}},"canonical_sha256":"38535a5752bb1132fedec5957dab07dcd3a39e32883219ee38bb4ce67ad7ef17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38535a5752bb1132fedec5957dab07dcd3a39e32883219ee38bb4ce67ad7ef17","first_computed_at":"2026-07-05T01:11:25.723075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:11:25.723075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CXK+KSixAj2qWSEC+2ZHTY7UwaahH3aIcn1B86uTgnbxLS+bwwqiCe8BWRBI6t53l/kz+3uDWroRyH2S1E4YAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:11:25.723435Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.10830","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c51d507ebb4e5dec371daf911b470cc7ea799aff50b197dbab2964ca1419dcae","sha256:1dfe8074f870c03041f764ee4f03b2a478e59915fa85ae6d88d9c0e7f300a63a"],"state_sha256":"c2dbae82c8fea5aa3f37a4d04606d7bd78dc4579d85e254f06e6b38b8843374a"}