{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:2GEOAXYP3XCKLBSUFKWD46BNDV","short_pith_number":"pith:2GEOAXYP","schema_version":"1.0","canonical_sha256":"d188e05f0fddc4a586542aac3e782d1d49b978a940a36ba390011bdf038691ef","source":{"kind":"arxiv","id":"0912.1419","version":2},"attestation_state":"computed","paper":{"title":"On the Kleinman-Martin integral equation method for electromagnetic scattering by a dielectric body","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Fr\\'ed\\'erique Le Lou\\\"er (IRMAR), Martin Costabel (IRMAR)","submitted_at":"2009-12-08T07:25:12Z","abstract_excerpt":"The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the interface $\\Gamma$. In this paper, following an idea developed by Kleinman and Martin \\cite{KlMa} for acoustic scattering problems, we consider methods for solving the dielectric scattering problem using a single integral equation over $\\Gamma$ for a single unknown density. One knows that such boundary integral formulations of the Maxwell equations are not uniquely "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0912.1419","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-12-08T07:25:12Z","cross_cats_sorted":[],"title_canon_sha256":"fd3f8a7682a77b3148189ddfc2bf19b52a0b7178863c04bdaf25ce84abc73d3a","abstract_canon_sha256":"57cbc8abee5477d0a166449d57c805906a16ea0901a6b5f2ce5b6acd7b9885c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:57.200848Z","signature_b64":"d7UpytEO6NNYZJr5ayI26htgmkaaxlDvThoTnpJbItZ7MM+sS0GkdkQCgUV8s7vPHgwV6QzaG8fJyEz2L6krBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d188e05f0fddc4a586542aac3e782d1d49b978a940a36ba390011bdf038691ef","last_reissued_at":"2026-05-18T04:27:57.200242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:57.200242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Kleinman-Martin integral equation method for electromagnetic scattering by a dielectric body","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Fr\\'ed\\'erique Le Lou\\\"er (IRMAR), Martin Costabel (IRMAR)","submitted_at":"2009-12-08T07:25:12Z","abstract_excerpt":"The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the interface $\\Gamma$. In this paper, following an idea developed by Kleinman and Martin \\cite{KlMa} for acoustic scattering problems, we consider methods for solving the dielectric scattering problem using a single integral equation over $\\Gamma$ for a single unknown density. One knows that such boundary integral formulations of the Maxwell equations are not uniquely "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1419","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0912.1419","created_at":"2026-05-18T04:27:57.200325+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.1419v2","created_at":"2026-05-18T04:27:57.200325+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.1419","created_at":"2026-05-18T04:27:57.200325+00:00"},{"alias_kind":"pith_short_12","alias_value":"2GEOAXYP3XCK","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"2GEOAXYP3XCKLBSU","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"2GEOAXYP","created_at":"2026-05-18T12:25:58.018023+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2GEOAXYP3XCKLBSUFKWD46BNDV","json":"https://pith.science/pith/2GEOAXYP3XCKLBSUFKWD46BNDV.json","graph_json":"https://pith.science/api/pith-number/2GEOAXYP3XCKLBSUFKWD46BNDV/graph.json","events_json":"https://pith.science/api/pith-number/2GEOAXYP3XCKLBSUFKWD46BNDV/events.json","paper":"https://pith.science/paper/2GEOAXYP"},"agent_actions":{"view_html":"https://pith.science/pith/2GEOAXYP3XCKLBSUFKWD46BNDV","download_json":"https://pith.science/pith/2GEOAXYP3XCKLBSUFKWD46BNDV.json","view_paper":"https://pith.science/paper/2GEOAXYP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.1419&json=true","fetch_graph":"https://pith.science/api/pith-number/2GEOAXYP3XCKLBSUFKWD46BNDV/graph.json","fetch_events":"https://pith.science/api/pith-number/2GEOAXYP3XCKLBSUFKWD46BNDV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2GEOAXYP3XCKLBSUFKWD46BNDV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2GEOAXYP3XCKLBSUFKWD46BNDV/action/storage_attestation","attest_author":"https://pith.science/pith/2GEOAXYP3XCKLBSUFKWD46BNDV/action/author_attestation","sign_citation":"https://pith.science/pith/2GEOAXYP3XCKLBSUFKWD46BNDV/action/citation_signature","submit_replication":"https://pith.science/pith/2GEOAXYP3XCKLBSUFKWD46BNDV/action/replication_record"}},"created_at":"2026-05-18T04:27:57.200325+00:00","updated_at":"2026-05-18T04:27:57.200325+00:00"}