{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:T65O3LG7XKPYHXIWHZWUIX45DV","short_pith_number":"pith:T65O3LG7","schema_version":"1.0","canonical_sha256":"9fbaedacdfba9f83dd163e6d445f9d1d7f06338a16bb1cea676ea92ce997b5d9","source":{"kind":"arxiv","id":"1701.07957","version":3},"attestation_state":"computed","paper":{"title":"On vanishing near corners of transmission eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Eemeli Bl{\\aa}sten, Hongyu Liu","submitted_at":"2017-01-27T06:53:51Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in $\\mathbb{R}^n$, $n\\geq 2$, and $V\\in L^\\infty(\\Omega)$ be a potential function. Consider the following transmission eigenvalue problem for nontrivial $v, w\\in L^2(\\Omega)$ and $k\\in\\mathbb{R}_+$, \\[(\\Delta+k^2)v= 0 \\quad \\text{in } \\Omega,\\] \\[(\\Delta+k^2(1+V))w= 0 \\quad \\text{in } \\Omega,\\] \\[w-v \\in H^2_0(\\Omega), \\quad \\lVert v \\rVert_{L^2(\\Omega)}=1. \\] We show that the transmission eigenfunctions $v$ and $w$ carry the geometric information of $\\mathrm{supp}(V)$. Indeed, it is proved that $v$ and $w$ vanish near a corner point on $\\partial \\Omega$ in a g"},"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":"1701.07957","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-27T06:53:51Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"75a3abf915f900a93e423ea779cb52f6ca8a846d1375d9d25914b214e6e56c8d","abstract_canon_sha256":"c3e1eabeb38581de5b0853615a9d8df334b2fcf3fc6bf0121d6d43290ba09413"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:13.926458Z","signature_b64":"J+wDMrxif5tD6Zu91r0H+jmRBPmUVdgJ9gM6YVW0WG4CUHjtpPhkU+Nh+73uPsUGe4fptlsdS4XuvlQfzTRjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fbaedacdfba9f83dd163e6d445f9d1d7f06338a16bb1cea676ea92ce997b5d9","last_reissued_at":"2026-05-18T00:32:13.925897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:13.925897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On vanishing near corners of transmission eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Eemeli Bl{\\aa}sten, Hongyu Liu","submitted_at":"2017-01-27T06:53:51Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in $\\mathbb{R}^n$, $n\\geq 2$, and $V\\in L^\\infty(\\Omega)$ be a potential function. Consider the following transmission eigenvalue problem for nontrivial $v, w\\in L^2(\\Omega)$ and $k\\in\\mathbb{R}_+$, \\[(\\Delta+k^2)v= 0 \\quad \\text{in } \\Omega,\\] \\[(\\Delta+k^2(1+V))w= 0 \\quad \\text{in } \\Omega,\\] \\[w-v \\in H^2_0(\\Omega), \\quad \\lVert v \\rVert_{L^2(\\Omega)}=1. \\] We show that the transmission eigenfunctions $v$ and $w$ carry the geometric information of $\\mathrm{supp}(V)$. Indeed, it is proved that $v$ and $w$ vanish near a corner point on $\\partial \\Omega$ in a g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07957","kind":"arxiv","version":3},"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":"1701.07957","created_at":"2026-05-18T00:32:13.925966+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.07957v3","created_at":"2026-05-18T00:32:13.925966+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07957","created_at":"2026-05-18T00:32:13.925966+00:00"},{"alias_kind":"pith_short_12","alias_value":"T65O3LG7XKPY","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"T65O3LG7XKPYHXIW","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"T65O3LG7","created_at":"2026-05-18T12:31:43.269735+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/T65O3LG7XKPYHXIWHZWUIX45DV","json":"https://pith.science/pith/T65O3LG7XKPYHXIWHZWUIX45DV.json","graph_json":"https://pith.science/api/pith-number/T65O3LG7XKPYHXIWHZWUIX45DV/graph.json","events_json":"https://pith.science/api/pith-number/T65O3LG7XKPYHXIWHZWUIX45DV/events.json","paper":"https://pith.science/paper/T65O3LG7"},"agent_actions":{"view_html":"https://pith.science/pith/T65O3LG7XKPYHXIWHZWUIX45DV","download_json":"https://pith.science/pith/T65O3LG7XKPYHXIWHZWUIX45DV.json","view_paper":"https://pith.science/paper/T65O3LG7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.07957&json=true","fetch_graph":"https://pith.science/api/pith-number/T65O3LG7XKPYHXIWHZWUIX45DV/graph.json","fetch_events":"https://pith.science/api/pith-number/T65O3LG7XKPYHXIWHZWUIX45DV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T65O3LG7XKPYHXIWHZWUIX45DV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T65O3LG7XKPYHXIWHZWUIX45DV/action/storage_attestation","attest_author":"https://pith.science/pith/T65O3LG7XKPYHXIWHZWUIX45DV/action/author_attestation","sign_citation":"https://pith.science/pith/T65O3LG7XKPYHXIWHZWUIX45DV/action/citation_signature","submit_replication":"https://pith.science/pith/T65O3LG7XKPYHXIWHZWUIX45DV/action/replication_record"}},"created_at":"2026-05-18T00:32:13.925966+00:00","updated_at":"2026-05-18T00:32:13.925966+00:00"}