{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OQ4AJEKW6HKSBLKBHKI6UVOH46","short_pith_number":"pith:OQ4AJEKW","schema_version":"1.0","canonical_sha256":"7438049156f1d520ad413a91ea55c7e783c969b6ce3833d4d02eb453ed3aad81","source":{"kind":"arxiv","id":"1312.1481","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic analysis of the transmission eigenvalue problem for a Dirichlet obstacle coated by a thin layer of non-absorbing media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fioralba Cakoni, Houssem Haddar, Nicolas Chaulet","submitted_at":"2013-12-05T09:41:57Z","abstract_excerpt":"We consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first transmission eigenvalue with respect to the thickness of the thin layer. Our convergence analysis is based on a Max-Min principle and an iterative approach which involves estimates on the corresponding eigenfunctions. We provide explicit expressions for the terms in the asymptotic expansion up to order three."},"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":"1312.1481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-05T09:41:57Z","cross_cats_sorted":[],"title_canon_sha256":"60f80fa47dea9661686854102b7cd882ae00aea7c1e8ab54d09cfd34c0e8c5c8","abstract_canon_sha256":"90aa813e8fd7c58ef50b71423450bf12e3ba30a9da1ce89f61b14f9725bfb635"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:27.177102Z","signature_b64":"i4s8jj8/PS3OoChC63+Cec/MUU4zxx9DBTRic8+ODBqggAHq9/lXceSz/mdVVCLSajth7bxX5jUXXmNPXquSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7438049156f1d520ad413a91ea55c7e783c969b6ce3833d4d02eb453ed3aad81","last_reissued_at":"2026-05-18T03:05:27.176586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:27.176586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic analysis of the transmission eigenvalue problem for a Dirichlet obstacle coated by a thin layer of non-absorbing media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fioralba Cakoni, Houssem Haddar, Nicolas Chaulet","submitted_at":"2013-12-05T09:41:57Z","abstract_excerpt":"We consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first transmission eigenvalue with respect to the thickness of the thin layer. Our convergence analysis is based on a Max-Min principle and an iterative approach which involves estimates on the corresponding eigenfunctions. We provide explicit expressions for the terms in the asymptotic expansion up to order three."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1481","kind":"arxiv","version":1},"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":"1312.1481","created_at":"2026-05-18T03:05:27.176663+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.1481v1","created_at":"2026-05-18T03:05:27.176663+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1481","created_at":"2026-05-18T03:05:27.176663+00:00"},{"alias_kind":"pith_short_12","alias_value":"OQ4AJEKW6HKS","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OQ4AJEKW6HKSBLKB","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OQ4AJEKW","created_at":"2026-05-18T12:27:54.935989+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/OQ4AJEKW6HKSBLKBHKI6UVOH46","json":"https://pith.science/pith/OQ4AJEKW6HKSBLKBHKI6UVOH46.json","graph_json":"https://pith.science/api/pith-number/OQ4AJEKW6HKSBLKBHKI6UVOH46/graph.json","events_json":"https://pith.science/api/pith-number/OQ4AJEKW6HKSBLKBHKI6UVOH46/events.json","paper":"https://pith.science/paper/OQ4AJEKW"},"agent_actions":{"view_html":"https://pith.science/pith/OQ4AJEKW6HKSBLKBHKI6UVOH46","download_json":"https://pith.science/pith/OQ4AJEKW6HKSBLKBHKI6UVOH46.json","view_paper":"https://pith.science/paper/OQ4AJEKW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.1481&json=true","fetch_graph":"https://pith.science/api/pith-number/OQ4AJEKW6HKSBLKBHKI6UVOH46/graph.json","fetch_events":"https://pith.science/api/pith-number/OQ4AJEKW6HKSBLKBHKI6UVOH46/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OQ4AJEKW6HKSBLKBHKI6UVOH46/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OQ4AJEKW6HKSBLKBHKI6UVOH46/action/storage_attestation","attest_author":"https://pith.science/pith/OQ4AJEKW6HKSBLKBHKI6UVOH46/action/author_attestation","sign_citation":"https://pith.science/pith/OQ4AJEKW6HKSBLKBHKI6UVOH46/action/citation_signature","submit_replication":"https://pith.science/pith/OQ4AJEKW6HKSBLKBHKI6UVOH46/action/replication_record"}},"created_at":"2026-05-18T03:05:27.176663+00:00","updated_at":"2026-05-18T03:05:27.176663+00:00"}