{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OAODLIXJHVBNJYYZP6V4UYN2Q7","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":"2d1d865e8b842d0f52a1642101b21c7d34d147890bd7b85b045b640669a05607","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-09T02:40:34Z","title_canon_sha256":"593bee8bc354241201b7cdced6e10605bed449ef4fea6b2f4efca6809a475df7"},"schema_version":"1.0","source":{"id":"2506.07370","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07370","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07370v1","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07370","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"OAODLIXJHVBN","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"pith_short_16","alias_value":"OAODLIXJHVBNJYYZ","created_at":"2026-07-05T11:18:25Z"},{"alias_kind":"pith_short_8","alias_value":"OAODLIXJ","created_at":"2026-07-05T11:18:25Z"}],"graph_snapshots":[{"event_id":"sha256:4e3be7e37ab530db1551d91ca8d9dc0ef36dd6c3039b4d06ea31da464ef3e64d","target":"graph","created_at":"2026-07-05T11:18:25Z","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/2506.07370/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we numerically investigate the inverse Robin problem of recovering a piecewise constant Robin coefficient in an elliptic or parabolic problem from the Cauchy data on a part of the boundary, a problem that commonly arises in applications such as non-destructive corrosion detection. We employ a Kohn-Vogelius type variational functional for the regularized reconstruction, and discretize the resulting optimization problem using the Galerkin finite element method on a graded mesh. We establish rigorous error estimates on the recovered Robin coefficient in terms of the mesh size, tempo","authors_text":"Bangti Jin, Erik Burman, Siyu Cen, Zhi Zhou","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-09T02:40:34Z","title":"Numerical Approximation and Analysis of the Inverse Robin Problem Using the Kohn-Vogelius Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07370","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:fc2fb47bdb09f31525b4c250d2874c6bc0e7be18398d62e69e2cad1ed41e1b5b","target":"record","created_at":"2026-07-05T11:18:25Z","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":"2d1d865e8b842d0f52a1642101b21c7d34d147890bd7b85b045b640669a05607","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-09T02:40:34Z","title_canon_sha256":"593bee8bc354241201b7cdced6e10605bed449ef4fea6b2f4efca6809a475df7"},"schema_version":"1.0","source":{"id":"2506.07370","kind":"arxiv","version":1}},"canonical_sha256":"701c35a2e93d42d4e3197fabca61ba87fb89e4c06fb93d913304bcee86e51c3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"701c35a2e93d42d4e3197fabca61ba87fb89e4c06fb93d913304bcee86e51c3e","first_computed_at":"2026-07-05T11:18:25.958814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:25.958814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BpzZm0Q8moiW6oA239rJmbyyRUKsy7JBLASbxQaZELmFKQ2FKw2axmcROAZG0ded9xNGizHN6UuKFEqTlBhPBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:25.959366Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc2fb47bdb09f31525b4c250d2874c6bc0e7be18398d62e69e2cad1ed41e1b5b","sha256:4e3be7e37ab530db1551d91ca8d9dc0ef36dd6c3039b4d06ea31da464ef3e64d"],"state_sha256":"d6173fa9ab34c66c7155efbcfdf1dcc2ca2d2b3f06d3beecac28e754ae5ac238"}