{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:RNXD5TF6QY2YUG6VKNOCEXCE6E","short_pith_number":"pith:RNXD5TF6","schema_version":"1.0","canonical_sha256":"8b6e3eccbe86358a1bd5535c225c44f10cb266abfd74bd5c8710b138928d3dd6","source":{"kind":"arxiv","id":"1305.0720","version":1},"attestation_state":"computed","paper":{"title":"The Dirichlet-to-Neumann operator via hidden compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.F.M. ter Elst, J.B. Kennedy, M. Sauter, W. Arendt","submitted_at":"2013-05-03T14:25:19Z","abstract_excerpt":"We show that to each symmetric elliptic operator of the form \\[ \\mathcal{A} = - \\sum \\partial_k \\, a_{kl} \\, \\partial_l + c \\] on a bounded Lipschitz domain $\\Omega \\subset \\mathbb{R}^d$ one can associate a self-adjoint Dirichlet-to-Neumann operator on $L_2(\\partial \\Omega)$, which may be multi-valued if 0 is in the Dirichlet spectrum of $\\mathcal{A}$. To overcome the lack of coerciveness in this case, we employ a new version of the Lax--Milgram lemma based on an indirect ellipticity property that we call hidden compactness. We then establish uniform resolvent convergence of a sequence of Diri"},"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":"1305.0720","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-03T14:25:19Z","cross_cats_sorted":[],"title_canon_sha256":"8693b5bd666ef823422d696c9a50a3fedd77891e69b6965fcbfbaec29643aa74","abstract_canon_sha256":"ee31e64dd0e13033d66a59c5b8a45ed696757399ab1408bc98f6f8f989cfd183"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:34.044240Z","signature_b64":"NVMKAuDdRWMInWCEOj1CNjJU5Qa1M0KUox/6axth+IDGLhXAzfUCsl+eqhI7H6uux/dTbbnQUJGJKl/aCrCeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b6e3eccbe86358a1bd5535c225c44f10cb266abfd74bd5c8710b138928d3dd6","last_reissued_at":"2026-05-18T02:17:34.043440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:34.043440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Dirichlet-to-Neumann operator via hidden compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.F.M. ter Elst, J.B. Kennedy, M. Sauter, W. Arendt","submitted_at":"2013-05-03T14:25:19Z","abstract_excerpt":"We show that to each symmetric elliptic operator of the form \\[ \\mathcal{A} = - \\sum \\partial_k \\, a_{kl} \\, \\partial_l + c \\] on a bounded Lipschitz domain $\\Omega \\subset \\mathbb{R}^d$ one can associate a self-adjoint Dirichlet-to-Neumann operator on $L_2(\\partial \\Omega)$, which may be multi-valued if 0 is in the Dirichlet spectrum of $\\mathcal{A}$. To overcome the lack of coerciveness in this case, we employ a new version of the Lax--Milgram lemma based on an indirect ellipticity property that we call hidden compactness. We then establish uniform resolvent convergence of a sequence of Diri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0720","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":"1305.0720","created_at":"2026-05-18T02:17:34.043588+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0720v1","created_at":"2026-05-18T02:17:34.043588+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0720","created_at":"2026-05-18T02:17:34.043588+00:00"},{"alias_kind":"pith_short_12","alias_value":"RNXD5TF6QY2Y","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"RNXD5TF6QY2YUG6V","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"RNXD5TF6","created_at":"2026-05-18T12:27:59.945178+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/RNXD5TF6QY2YUG6VKNOCEXCE6E","json":"https://pith.science/pith/RNXD5TF6QY2YUG6VKNOCEXCE6E.json","graph_json":"https://pith.science/api/pith-number/RNXD5TF6QY2YUG6VKNOCEXCE6E/graph.json","events_json":"https://pith.science/api/pith-number/RNXD5TF6QY2YUG6VKNOCEXCE6E/events.json","paper":"https://pith.science/paper/RNXD5TF6"},"agent_actions":{"view_html":"https://pith.science/pith/RNXD5TF6QY2YUG6VKNOCEXCE6E","download_json":"https://pith.science/pith/RNXD5TF6QY2YUG6VKNOCEXCE6E.json","view_paper":"https://pith.science/paper/RNXD5TF6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0720&json=true","fetch_graph":"https://pith.science/api/pith-number/RNXD5TF6QY2YUG6VKNOCEXCE6E/graph.json","fetch_events":"https://pith.science/api/pith-number/RNXD5TF6QY2YUG6VKNOCEXCE6E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RNXD5TF6QY2YUG6VKNOCEXCE6E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RNXD5TF6QY2YUG6VKNOCEXCE6E/action/storage_attestation","attest_author":"https://pith.science/pith/RNXD5TF6QY2YUG6VKNOCEXCE6E/action/author_attestation","sign_citation":"https://pith.science/pith/RNXD5TF6QY2YUG6VKNOCEXCE6E/action/citation_signature","submit_replication":"https://pith.science/pith/RNXD5TF6QY2YUG6VKNOCEXCE6E/action/replication_record"}},"created_at":"2026-05-18T02:17:34.043588+00:00","updated_at":"2026-05-18T02:17:34.043588+00:00"}