Einstein-Hilbert Density on an Eigenvalue-Rigid Tensor Orbit

We study a Landau-Wilson model for a symmetric tensor order parameter η ∈ Sym²(ℝ⁴) with global O(4) symmetry and a stationary vacuum with Lorentzian signature. The Goldstone sector is the orbit O(4)/(O(3) × Z₂), an eigenvalue-rigid unimodular submanifold. On the frozen single-gradient sector, the sigma-model kinetic density is exactly proportional to the Einstein-Hilbert density, off shell and at finite field amplitude. The result is not a derivation of general relativity: the strict Goldstone sector has three massless modes, and generic Lorentzian geometries lie outside the orbit. The parent tensor theory supplies the missing eigenvalue-changing directions as seven massive normal modes with canonical spectrum 10×5, 10 − 4√3, and 10 + 4√3. The deposit includes LaTeX source, compiled PDF, and an independent SymPy symbolic verification of the central identity.