We consider the algebra $\dotΣ(\mathcal L)$ generated by the inner-limit derivations over the ${\rm GICAR}$ algebra of a fermion gas populating an aperiodic Delone set $\mathcal L$. Under standard physical assumptions such as finite interaction range, Galilean invariance and continuity with respect to the aperiodic lattice, we demonstrate that the image of $\dot Σ(\mathcal L)$ through the Fock representation can be completed to a groupoid-solvable pro-$C^\ast$-algebra. Our result is the first

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... ep towards unlocking the $K$-theoretic tools available for separable $C^\ast$-algebra for applications in the context of interacting fermions.