Lattice-isomorphism conjecture for symmetric-power quotients of $Q^*$

Let $d,e,n\in\mathbb{N}$ satisfy the hypotheses of Corollary $$. Consider the lattices of subobjects of

$$Q^n/Q^n[d-1]\qquad\text{and}\qquad Q^{n+e-d}/Q^{n+e-d}[e-1].$$

Lattice-isomorphism conjecture. These lattices are isomorphic, compatibly with the identification predicted by the periodicity conjecture for the corresponding Grothendieck-group classes.

This strengthens the preceding periodicity conjecture from an equality of Grothendieck-group classes to an isomorphism of subobject lattices. The source gives no general resolution; it follows in the range $n-d\leq 5$ insofar as the preceding conjecture is established there, but remains open in general.