The unitary-invariance conjecture for partial ideals of $C^*$-algebras

Let $\mathcal{A}$ be a unital $C^*$-algebra. A partial ideal is a choice of a closed ideal $I_V$ in each unital commutative sub-$C^*$-algebra $V\subset\mathcal{A}$ such that, whenever $V\subset V'$, one has $I_V=I_{V'}\cap V$. A total ideal is a closed two-sided ideal of $\mathcal{A}$. Unitary-invariance conjecture. A partial ideal of a unital $C^*$-algebra arises from a total ideal if and only if it is fixed by every unitary rotation, meaning that $I_{uVu^*}=uI_Vu^*$ for every unitary $u$. This criterion would characterize precisely the partial ideals corresponding to closed two-sided ideals and would imply the closed-sets extension conjecture. The source does not state a resolution.