Quotient–submodule equidistribution conjecture

For every finite-dimensional representation-finite algebra $A$ and every integer $i\ge 0$, the number of quotient-closed full additive subcategories $\mathcal{C}\subseteq \operatorname{mod}A$ satisfying $|\operatorname{ind}(\mathcal{C})|=i$ equals the number of submodule-closed full additive subcategories $\mathcal{D}\subseteq \operatorname{mod}A$ satisfying $|\operatorname{ind}(\mathcal{D})|=i$. Here quotient-closed means closed under factor modules, submodule-closed means closed under submodules, and $|\operatorname{ind}(\mathcal{C})|$ denotes the number of isomorphism classes of indecomposable modules in $\mathcal{C}$, with analogous notation for $\mathcal{D}$.