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This is a generalization of \\cite{Chr-tri} to higher dimensions. Again it is {\\it not} an asymptotic, but an exact formula. The proof is by simple integrations by parts and linear algebra.\n  We also consider the following inverse problem: do the {\\it norms} of the Neumann data on a simplex determine a constant coeff"},"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":"1704.02048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-06T23:27:53Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"735e66808df7d9377f48162c64a52a5cc070f683516c96e6db3eda83977f92a7","abstract_canon_sha256":"23d50472664051ff347d06a85f8bbe7012e6190a56dc7aebca4d4b70b7a0496b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:50.924455Z","signature_b64":"IvsVW23Qv2CxrJpLgPh4VGYb8Qiteker5EtlQdoYRLXcAEwcmFgyUPdzOFP1tAaJNEskEcNGHr0Tph+H5T9IAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be83aefa543b49be711f9b7ffabf352aa9a619177f1db8398aed6c04df3913eb","last_reissued_at":"2026-05-18T00:46:50.923670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:50.923670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equidistribution of Neumann data mass on simplices and a simple inverse problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Hans Christianson","submitted_at":"2017-04-06T23:27:53Z","abstract_excerpt":"In this paper we study the behaviour of the Neumann data of Dirichlet eigenfunctions on simplices. 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