Algebraic packing property conjecture for uniform clutters

Let $\mathcal C$ be a uniform clutter with incidence vectors $v_1,\ldots,v_q$, and let $P$ be the associated polytope. The clutter satisfies the packing property if every minor satisfies the König property. Let $K[Ft]$ denote the homogeneous ring generated by the clutter's edge monomials, and let $A(P)$ denote the Ehrhart ring of $P$. Algebraic packing property conjecture. If $\mathcal C$ is a uniform clutter with the packing property, then

$$K[Ft]=A(P).$$

This is presented as an algebraic version of the Conforti–Cornuéjols conjecture, using the stated characterization of the relevant ring-theoretic condition. Its resolution status is not specified in the candidate span or accompanying text.