Generic-condition conjecture for periodic Schrödinger potentials

Let $H_0=-\Delta+q(x)$ be a Schrödinger operator with periodic potential $q$, let $F_{\,\lambda}(q)$ be its Fermi variety, and let the Condition mean that, for every $\lambda$ in the interior of a spectral band, every irreducible component of $F_{\,\lambda}(q)$ intersects the real space $\mathbb{R}^n$ in a subset of dimension $n-1$, equivalently one containing a piece of a smooth hypersurface. Generic-condition conjecture. A generic periodic potential from an appropriate functional class satisfies the Condition. The conjecture is presented as a weaker version of the preceding irreducibility conjecture and is intended to provide the hypothesis needed for the paper's conditional absence-of-embedded-eigenvalues result; it remains unproved in the source.