{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LGUQ7RMBUKPOIRRYHJCTMP76JI","short_pith_number":"pith:LGUQ7RMB","schema_version":"1.0","canonical_sha256":"59a90fc581a29ee446383a45363ffe4a3c365417da15b18ca1e464bc08d71f83","source":{"kind":"arxiv","id":"2605.25579","version":1},"attestation_state":"computed","paper":{"title":"Shape Derivatives for Maxwell's Equations with Nonlinear Boundary Conditions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Deng, Yixian Gao","submitted_at":"2026-05-25T08:31:22Z","abstract_excerpt":"This paper develops a trace-regular variational framework for time-harmonic Maxwell scattering problems involving pointwise nonlinear boundary and interface responses. We investigate three canonical classes of models: nonlinear impedance, nonlinear perfect electric conductor, and nonlinear transmission conditions. Since the standard Maxwell tangential trace belongs to a space of negative order, the nonlinearities are formulated in refined functional spaces where the tangential electric field admits an $L^2(\\Gamma)$-trace. Under the assumption of a sufficiently small Lipschitz constant for the "},"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":"2605.25579","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-25T08:31:22Z","cross_cats_sorted":[],"title_canon_sha256":"cac16199216d69721e54dd9559aa34ed826e12e0945ba544f6bcf61fe822080c","abstract_canon_sha256":"687b449ac32dd5bbe2e413671e437d341735181f401f052f392ad84aa2d8cbd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:44.005426Z","signature_b64":"iwAH1s0Bic6S3aN0+rQv6fDP0dVEBUw0XjvjniF62c8L6BoBrhpehjJGJqESyPp/4Mhgn8aFye9qFJPF4vT/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59a90fc581a29ee446383a45363ffe4a3c365417da15b18ca1e464bc08d71f83","last_reissued_at":"2026-05-26T02:04:44.004590Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:44.004590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shape Derivatives for Maxwell's Equations with Nonlinear Boundary Conditions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Deng, Yixian Gao","submitted_at":"2026-05-25T08:31:22Z","abstract_excerpt":"This paper develops a trace-regular variational framework for time-harmonic Maxwell scattering problems involving pointwise nonlinear boundary and interface responses. We investigate three canonical classes of models: nonlinear impedance, nonlinear perfect electric conductor, and nonlinear transmission conditions. Since the standard Maxwell tangential trace belongs to a space of negative order, the nonlinearities are formulated in refined functional spaces where the tangential electric field admits an $L^2(\\Gamma)$-trace. Under the assumption of a sufficiently small Lipschitz constant for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25579","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25579/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.25579","created_at":"2026-05-26T02:04:44.004733+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.25579v1","created_at":"2026-05-26T02:04:44.004733+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25579","created_at":"2026-05-26T02:04:44.004733+00:00"},{"alias_kind":"pith_short_12","alias_value":"LGUQ7RMBUKPO","created_at":"2026-05-26T02:04:44.004733+00:00"},{"alias_kind":"pith_short_16","alias_value":"LGUQ7RMBUKPOIRRY","created_at":"2026-05-26T02:04:44.004733+00:00"},{"alias_kind":"pith_short_8","alias_value":"LGUQ7RMB","created_at":"2026-05-26T02:04:44.004733+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/LGUQ7RMBUKPOIRRYHJCTMP76JI","json":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI.json","graph_json":"https://pith.science/api/pith-number/LGUQ7RMBUKPOIRRYHJCTMP76JI/graph.json","events_json":"https://pith.science/api/pith-number/LGUQ7RMBUKPOIRRYHJCTMP76JI/events.json","paper":"https://pith.science/paper/LGUQ7RMB"},"agent_actions":{"view_html":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI","download_json":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI.json","view_paper":"https://pith.science/paper/LGUQ7RMB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.25579&json=true","fetch_graph":"https://pith.science/api/pith-number/LGUQ7RMBUKPOIRRYHJCTMP76JI/graph.json","fetch_events":"https://pith.science/api/pith-number/LGUQ7RMBUKPOIRRYHJCTMP76JI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI/action/storage_attestation","attest_author":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI/action/author_attestation","sign_citation":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI/action/citation_signature","submit_replication":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI/action/replication_record"}},"created_at":"2026-05-26T02:04:44.004733+00:00","updated_at":"2026-05-26T02:04:44.004733+00:00"}