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We prove that the nonlinear Dirichlet-to-Neumann map determines the positive smooth source from its values on the restricted large-data rays $t\\phi_E|_{\\partial\\Omega}$, where $E\\in Gr(k-1,n)$, $\\phi_E(x)=|P_Ex|^2/2$, and $t$ is sufficiently large. The Hessian of each boundary profile has exactly $k-1$ large directions and is flat on $V=E^\\perp$. Thus, the leading "},"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":"2607.04662","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-06T04:32:07Z","cross_cats_sorted":[],"title_canon_sha256":"3af7ab64f3b588059c0b9e96bd1a53d9f4b6765b289c6c9eedb4bcdaa9102b26","abstract_canon_sha256":"5bee45b94ae13ff50cdee4188ef00f3a0bf4b980856013bbb3e3a46896a3186d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:19:30.010345Z","signature_b64":"JtnnS2NzI36jhsLXtLlHcBB7ETGsM++LeckbIpVyDJdg4AmFZhI841H9Q6FClM2OUl14IGyJk282L+2PreqSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f4d04064ed0ff9d20c992ad3e416b1dbcb89591372aac059334de1624f3c8ef","last_reissued_at":"2026-07-07T02:19:30.009779Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:19:30.009779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Affine section tomography for inverse source problems in $k$-Hessian equations with restricted large boundary data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yi-Hsuan Lin","submitted_at":"2026-07-06T04:32:07Z","abstract_excerpt":"We consider an inverse source problem for the $k$-Hessian equation\n  \\begin{equation*}\n  \\sigma_k(D^2u)=f(x)\n  \\end{equation*}\n  on the $k$-admissible branch in a smooth uniformly convex domain in $\\mathbb R^n$, where $2\\le k\\le n$. We prove that the nonlinear Dirichlet-to-Neumann map determines the positive smooth source from its values on the restricted large-data rays $t\\phi_E|_{\\partial\\Omega}$, where $E\\in Gr(k-1,n)$, $\\phi_E(x)=|P_Ex|^2/2$, and $t$ is sufficiently large. The Hessian of each boundary profile has exactly $k-1$ large directions and is flat on $V=E^\\perp$. 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