{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:5R54KDQPJZX72U566NXBPRYYF2","short_pith_number":"pith:5R54KDQP","schema_version":"1.0","canonical_sha256":"ec7bc50e0f4e6ffd53bef36e17c7182eb5a14a6495120974089e501f5aa4951b","source":{"kind":"arxiv","id":"1201.0690","version":3},"attestation_state":"computed","paper":{"title":"On Uniqueness in Electromagnetic Scattering from Biperiodic Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Armin Lechleiter, Dinh-Liem Nguyen","submitted_at":"2012-01-03T16:40:35Z","abstract_excerpt":"Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional non-trapping assumptions on the material parameter, this identity allows us to establish uniq"},"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":"1201.0690","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-03T16:40:35Z","cross_cats_sorted":[],"title_canon_sha256":"b03cd96c2ba9cd8561865c59e768d6846182f49da61a2d58b094669417b77d41","abstract_canon_sha256":"495f58135d4d727fb32f785e395d23c2fb392133197ddeb12d7de90a5a90c00b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:38.683957Z","signature_b64":"Z1FfzwRGWytgMhaCC5AR4ZYObaPxWCJIBSN5BLzKstiyskgMHo8kh0aOASRR5YwRh75ZOd980jDwoCYRAFYDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec7bc50e0f4e6ffd53bef36e17c7182eb5a14a6495120974089e501f5aa4951b","last_reissued_at":"2026-05-18T03:40:38.683241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:38.683241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Uniqueness in Electromagnetic Scattering from Biperiodic Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Armin Lechleiter, Dinh-Liem Nguyen","submitted_at":"2012-01-03T16:40:35Z","abstract_excerpt":"Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional non-trapping assumptions on the material parameter, this identity allows us to establish uniq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0690","kind":"arxiv","version":3},"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":"1201.0690","created_at":"2026-05-18T03:40:38.683359+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.0690v3","created_at":"2026-05-18T03:40:38.683359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0690","created_at":"2026-05-18T03:40:38.683359+00:00"},{"alias_kind":"pith_short_12","alias_value":"5R54KDQPJZX7","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"5R54KDQPJZX72U56","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"5R54KDQP","created_at":"2026-05-18T12:26:56.085431+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/5R54KDQPJZX72U566NXBPRYYF2","json":"https://pith.science/pith/5R54KDQPJZX72U566NXBPRYYF2.json","graph_json":"https://pith.science/api/pith-number/5R54KDQPJZX72U566NXBPRYYF2/graph.json","events_json":"https://pith.science/api/pith-number/5R54KDQPJZX72U566NXBPRYYF2/events.json","paper":"https://pith.science/paper/5R54KDQP"},"agent_actions":{"view_html":"https://pith.science/pith/5R54KDQPJZX72U566NXBPRYYF2","download_json":"https://pith.science/pith/5R54KDQPJZX72U566NXBPRYYF2.json","view_paper":"https://pith.science/paper/5R54KDQP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.0690&json=true","fetch_graph":"https://pith.science/api/pith-number/5R54KDQPJZX72U566NXBPRYYF2/graph.json","fetch_events":"https://pith.science/api/pith-number/5R54KDQPJZX72U566NXBPRYYF2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5R54KDQPJZX72U566NXBPRYYF2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5R54KDQPJZX72U566NXBPRYYF2/action/storage_attestation","attest_author":"https://pith.science/pith/5R54KDQPJZX72U566NXBPRYYF2/action/author_attestation","sign_citation":"https://pith.science/pith/5R54KDQPJZX72U566NXBPRYYF2/action/citation_signature","submit_replication":"https://pith.science/pith/5R54KDQPJZX72U566NXBPRYYF2/action/replication_record"}},"created_at":"2026-05-18T03:40:38.683359+00:00","updated_at":"2026-05-18T03:40:38.683359+00:00"}