Symplectic-capacity conjecture for Fermi ellipsoids

Let $\Psi$ be a quantum state such that the Fermi equation $g_{\mathrm{F}}(x,p)$ defines a hypersurface in phase space bounding a compact set $\Omega_{\mathrm{F}}$. A quantum blob is the phase-space object referred to in the conjecture, and $c$ denotes a symplectic capacity. Fermi-set capacity conjecture. There exists a symplectic capacity $c$ satisfying

$$c(\Omega_{\mathrm{F}})\geq\frac{1}{2}h$$

and the compact set $\Omega_{\mathrm{F}}$ contains a quantum blob. This conjecture extends the discussion of the Fermi function and associated Fermi ellipsoid beyond Gaussian states; the source provides no resolution of the claim.