{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VADG7D35DX5EEB2D7B7QG5IVQZ","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":"5705ba91faa7167425ab68db8b404a55ce77a764f3bca504294f43c202c63e1f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-01T09:30:43Z","title_canon_sha256":"aa4b68da2ea6048d3df4d5d5a062ae0147e8d3684ecd2e99f018b7814f53ddc2"},"schema_version":"1.0","source":{"id":"1103.0113","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0113","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0113v1","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0113","created_at":"2026-05-18T04:27:37Z"},{"alias_kind":"pith_short_12","alias_value":"VADG7D35DX5E","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"VADG7D35DX5EEB2D","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"VADG7D35","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:0073d2f0c3bbafb23075677004692947184aabfa3753dbb6136b2ae98d0ceedc","target":"graph","created_at":"2026-05-18T04:27:37Z","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"},"paper":{"abstract_excerpt":"We consider an operator $\\Delta^2 + A(x)\\cdot D+q(x)$ with the Navier boundary conditions on a bounded domain in $R^n$, $n\\ge 3$. We show that a first order perturbation $A(x)\\cdot D+q$ can be determined uniquely by measuring the Dirichlet--to--Neumann map on possibly very small subsets of the boundary of the domain. Notice that the corresponding result does not hold in general for a first order perturbation of the Laplacian.","authors_text":"Gunther Uhlmann, Katsiaryna Krupchyk, Matti Lassas","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-01T09:30:43Z","title":"Determining a first order perturbation of the biharmonic operator by partial boundary measurements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0113","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:dd8a42723b95362b3102313daaeaaa53b2f127cb055d82b92b8e535e8670cc8a","target":"record","created_at":"2026-05-18T04:27:37Z","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":"5705ba91faa7167425ab68db8b404a55ce77a764f3bca504294f43c202c63e1f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-01T09:30:43Z","title_canon_sha256":"aa4b68da2ea6048d3df4d5d5a062ae0147e8d3684ecd2e99f018b7814f53ddc2"},"schema_version":"1.0","source":{"id":"1103.0113","kind":"arxiv","version":1}},"canonical_sha256":"a8066f8f7d1dfa420743f87f037515865163604115add9f62bc24d70757e945f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8066f8f7d1dfa420743f87f037515865163604115add9f62bc24d70757e945f","first_computed_at":"2026-05-18T04:27:37.338799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:37.338799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XPUAVOh/u4XJ7hKSZS4QtN84f2foZFlfjHdNveecLaW7jtTo0JPIY7Q8snUBllB3V/UeJuR/mvNEy2u763mjCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:37.339441Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0113","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd8a42723b95362b3102313daaeaaa53b2f127cb055d82b92b8e535e8670cc8a","sha256:0073d2f0c3bbafb23075677004692947184aabfa3753dbb6136b2ae98d0ceedc"],"state_sha256":"634af48131dbe66dca883d97c4c443b9003293b5d7304067a52c5619c1d9c7ac"}