{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LGUQ7RMBUKPOIRRYHJCTMP76JI","short_pith_number":"pith:LGUQ7RMB","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"},"canonical_sha256":"59a90fc581a29ee446383a45363ffe4a3c365417da15b18ca1e464bc08d71f83","source":{"kind":"arxiv","id":"2605.25579","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25579","created_at":"2026-05-26T02:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25579v1","created_at":"2026-05-26T02:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25579","created_at":"2026-05-26T02:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"LGUQ7RMBUKPO","created_at":"2026-05-26T02:04:44Z"},{"alias_kind":"pith_short_16","alias_value":"LGUQ7RMBUKPOIRRY","created_at":"2026-05-26T02:04:44Z"},{"alias_kind":"pith_short_8","alias_value":"LGUQ7RMB","created_at":"2026-05-26T02:04:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LGUQ7RMBUKPOIRRYHJCTMP76JI","target":"record","payload":{"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"},"canonical_sha256":"59a90fc581a29ee446383a45363ffe4a3c365417da15b18ca1e464bc08d71f83","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"},"source_kind":"arxiv","source_id":"2605.25579","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-26T02:04:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3EyshhP41rcoGoix2rmif39itX0DpyqCF69NvUUzFiPEGZVxqLeeT3x/RSDfyec3GOE9DAzHMRfIpA9pQIRyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:09:30.315050Z"},"content_sha256":"7cced8fd2d3da5532fa0b32546abc14527a6a7453f7dd1094edda887546afb6b","schema_version":"1.0","event_id":"sha256:7cced8fd2d3da5532fa0b32546abc14527a6a7453f7dd1094edda887546afb6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LGUQ7RMBUKPOIRRYHJCTMP76JI","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-26T02:04:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+8YtvLlzVVJ7yYmhQuDW25Xi3yxzMNJEPgj9X9bisRTnyoOvc2kaRxLrpkKrpWfcHgPqsT9YGUnn4todH0J7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:09:30.315441Z"},"content_sha256":"d2c065730d1971761fdf52056e285347a8502d4076fd6e8a587d0d0400f98e06","schema_version":"1.0","event_id":"sha256:d2c065730d1971761fdf52056e285347a8502d4076fd6e8a587d0d0400f98e06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI/bundle.json","state_url":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T20:09:30Z","links":{"resolver":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI","bundle":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI/bundle.json","state":"https://pith.science/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LGUQ7RMBUKPOIRRYHJCTMP76JI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LGUQ7RMBUKPOIRRYHJCTMP76JI","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":"687b449ac32dd5bbe2e413671e437d341735181f401f052f392ad84aa2d8cbd9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-25T08:31:22Z","title_canon_sha256":"cac16199216d69721e54dd9559aa34ed826e12e0945ba544f6bcf61fe822080c"},"schema_version":"1.0","source":{"id":"2605.25579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25579","created_at":"2026-05-26T02:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25579v1","created_at":"2026-05-26T02:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25579","created_at":"2026-05-26T02:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"LGUQ7RMBUKPO","created_at":"2026-05-26T02:04:44Z"},{"alias_kind":"pith_short_16","alias_value":"LGUQ7RMBUKPOIRRY","created_at":"2026-05-26T02:04:44Z"},{"alias_kind":"pith_short_8","alias_value":"LGUQ7RMB","created_at":"2026-05-26T02:04:44Z"}],"graph_snapshots":[{"event_id":"sha256:d2c065730d1971761fdf52056e285347a8502d4076fd6e8a587d0d0400f98e06","target":"graph","created_at":"2026-05-26T02:04:44Z","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/2605.25579/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","authors_text":"Chao Deng, Yixian Gao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-25T08:31:22Z","title":"Shape Derivatives for Maxwell's Equations with Nonlinear Boundary Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25579","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":"sha256:7cced8fd2d3da5532fa0b32546abc14527a6a7453f7dd1094edda887546afb6b","target":"record","created_at":"2026-05-26T02:04:44Z","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":"687b449ac32dd5bbe2e413671e437d341735181f401f052f392ad84aa2d8cbd9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-25T08:31:22Z","title_canon_sha256":"cac16199216d69721e54dd9559aa34ed826e12e0945ba544f6bcf61fe822080c"},"schema_version":"1.0","source":{"id":"2605.25579","kind":"arxiv","version":1}},"canonical_sha256":"59a90fc581a29ee446383a45363ffe4a3c365417da15b18ca1e464bc08d71f83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59a90fc581a29ee446383a45363ffe4a3c365417da15b18ca1e464bc08d71f83","first_computed_at":"2026-05-26T02:04:44.004590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:44.004590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iwAH1s0Bic6S3aN0+rQv6fDP0dVEBUw0XjvjniF62c8L6BoBrhpehjJGJqESyPp/4Mhgn8aFye9qFJPF4vT/Cw==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:44.005426Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cced8fd2d3da5532fa0b32546abc14527a6a7453f7dd1094edda887546afb6b","sha256:d2c065730d1971761fdf52056e285347a8502d4076fd6e8a587d0d0400f98e06"],"state_sha256":"b48072effc0f3ca0bca741d2563b011076899d559b653a07fb42ce077698f1d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uhGfuXhAjEznj0waTMwZ3DojytyMfijmE/8cpjQzAnue5TUqATdUFMbFJ6bkMKV+VcPoscPDWG359LtZlVjuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:09:30.317393Z","bundle_sha256":"dde43a36b5d753c3ecc23358ff055dc51fffa25b121801fae61fa264e2565ec8"}}