A smooth strictly convex counterexample to exponential interior decay of Steklov eigenfunctions

We give an explicit bounded, simply connected planar domain with smooth strictly convex boundary on which uniform exponential interior decay of boundary-normalized Steklov eigenfunctions fails. At a fixed interior point, the squared eigenfunction values have no finite positive exponential spectral moment. The construction uses a conformal map with reciprocal boundary speed having nonnegative, subexponentially decaying Fourier coefficients. Positivity supplies lower bounds on all spectral moments, avoiding perturbative estimates of individual eigenfunctions. The result addresses the precise universal statement in Problem 024 of the AIM repository at the revision pinned in the references. All eigenfunctions and the domain in the proof are exact; finite-dimensional numerics are only supplementary.