The elastic Calderon problem in three dimensions: do boundary measurements determine smooth isotropic Lame moduli?

Theorem 1.1: on any bounded connected domain $\Omega\subset\mathbb R^3$ with $C^\infty$ boundary, if $\lambda_j,\mu_j\in C^\infty(\overline\Omega)$ satisfy $\mu_j>0$ , $3\lambda_j+2\mu_j>0$ and $\Lambda_{\lambda_1,\mu_1}=\Lambda_{\lambda_2,\mu_2}$ , then $\lambda_1=\lambda_2$ and $\mu_1=\mu_2$ . No analyticity, smallness or prior boundary agreement is assumed. It is a uniqueness theorem for smooth coefficients and full static data only: no reconstruction algorithm, no stability estimate, no partial-data or low-regularity version, and nothing about anisotropic elasticity.

Exact FrontierDelta

Prior state unknown→proved

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Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The elastic Calderon problem in three dimensions: do boundary measurements determine smooth isotropic Lame moduli? · 3D isotropic elastic Calderon problem

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VibeMathed record: The elastic Calderon problem in three dimensions: do boundary measurements determine smooth isotropic Lame moduli?

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No independent mathematician has checked this yet. Checked here: the introduction and Theorem 1.1 were read against the Nakamura-Uhlmann problem. lean/docs/372.md points to ComparatorChallenges/ElasticityUniqueness.json (theorem OAI.Elasticity.global_uniqueness, solution module OAI.MathematicalPhysics.Elasticity.Uniqueness); the solution file exists at the pinned commit and the challenge is not in formalization.yaml. The statement was read here: for every bounded connected open set in $\mathbb R^3$ with smooth boundary charts and moduli smooth up to the boundary with $\mu>0$ , $3\lambda+2\mu>0$ , equality of the variationally defined Dirichlet-to-Neumann pairings forces both moduli to agree on $\Omega$ . That is the headline claim. Not rebuilt here. The DN map is defined on a trace quotient rather than $H^{1/2}$ , as the file notes. No reconstruction or stability estimate is claimed.