{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:7ZTEDB7EOA63Y2RO6ZM5T5ULAQ","short_pith_number":"pith:7ZTEDB7E","schema_version":"1.0","canonical_sha256":"fe664187e4703dbc6a2ef659d9f68b040de30db673f817dbe924da45980d2962","source":{"kind":"arxiv","id":"2509.00455","version":1},"attestation_state":"computed","paper":{"title":"Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miles H. Wheeler","submitted_at":"2025-08-30T10:53:34Z","abstract_excerpt":"In this note we construct smooth bounded domains $\\Omega \\subset \\mathbb R^2$, other than disks, for which the overdetermined problem $$\n  \\left\\{\n  \\begin{alignedat}{2}\n  \\Delta u + \\lambda u &= 0 &\\qquad& \\text{ in } \\Omega, \\newline\n  u &= b &\\qquad& \\text{ on } \\partial \\Omega, \\newline\n  \\frac{\\partial u}{\\partial n} &= c &\\qquad& \\text{ on } \\partial \\Omega\n  \\end{alignedat}\n  \\right. $$ has a solution for some constants $\\lambda,b,c \\ne 0$. These appear to be the first counterexamples to a conjecture of Willms and Gladwell [WG94]."},"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":"2509.00455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-08-30T10:53:34Z","cross_cats_sorted":[],"title_canon_sha256":"7a175ff221e4228b48ad0e00bdd647fac213c81a4e32f1e1909f669e5a688f36","abstract_canon_sha256":"071328a226fbedc6813ff625325b2893e0ea117388a7d1b4ee3a0bf92f6a24a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:02:16.644082Z","signature_b64":"SA2GAYyBNxwOw+5uz+XLCAc2vUukKIO8mGDKoiCI7kbNo2P0D8AVi1JbL+k/kPpOQWUm6ZCd6rY5NB/FVp1hBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe664187e4703dbc6a2ef659d9f68b040de30db673f817dbe924da45980d2962","last_reissued_at":"2026-07-05T12:02:16.643612Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:02:16.643612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miles H. Wheeler","submitted_at":"2025-08-30T10:53:34Z","abstract_excerpt":"In this note we construct smooth bounded domains $\\Omega \\subset \\mathbb R^2$, other than disks, for which the overdetermined problem $$\n  \\left\\{\n  \\begin{alignedat}{2}\n  \\Delta u + \\lambda u &= 0 &\\qquad& \\text{ in } \\Omega, \\newline\n  u &= b &\\qquad& \\text{ on } \\partial \\Omega, \\newline\n  \\frac{\\partial u}{\\partial n} &= c &\\qquad& \\text{ on } \\partial \\Omega\n  \\end{alignedat}\n  \\right. $$ has a solution for some constants $\\lambda,b,c \\ne 0$. These appear to be the first counterexamples to a conjecture of Willms and Gladwell [WG94]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.00455","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/2509.00455/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2509.00455","created_at":"2026-07-05T12:02:16.643673+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.00455v1","created_at":"2026-07-05T12:02:16.643673+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.00455","created_at":"2026-07-05T12:02:16.643673+00:00"},{"alias_kind":"pith_short_12","alias_value":"7ZTEDB7EOA63","created_at":"2026-07-05T12:02:16.643673+00:00"},{"alias_kind":"pith_short_16","alias_value":"7ZTEDB7EOA63Y2RO","created_at":"2026-07-05T12:02:16.643673+00:00"},{"alias_kind":"pith_short_8","alias_value":"7ZTEDB7E","created_at":"2026-07-05T12:02:16.643673+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2602.07407","citing_title":"On two-dimensional steady compactly supported Euler flows with constant vorticity","ref_index":52,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ","json":"https://pith.science/pith/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ.json","graph_json":"https://pith.science/api/pith-number/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ/graph.json","events_json":"https://pith.science/api/pith-number/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ/events.json","paper":"https://pith.science/paper/7ZTEDB7E"},"agent_actions":{"view_html":"https://pith.science/pith/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ","download_json":"https://pith.science/pith/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ.json","view_paper":"https://pith.science/paper/7ZTEDB7E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.00455&json=true","fetch_graph":"https://pith.science/api/pith-number/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ/graph.json","fetch_events":"https://pith.science/api/pith-number/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ/action/storage_attestation","attest_author":"https://pith.science/pith/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ/action/author_attestation","sign_citation":"https://pith.science/pith/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ/action/citation_signature","submit_replication":"https://pith.science/pith/7ZTEDB7EOA63Y2RO6ZM5T5ULAQ/action/replication_record"}},"created_at":"2026-07-05T12:02:16.643673+00:00","updated_at":"2026-07-05T12:02:16.643673+00:00"}