Differential-operator conjecture for PA-forms

Let $X$ be a PA-space, let $f$ be a PA-form on $X$, let $\Omega(X)$ denote the space of smooth differential forms on $X$, and let $P$ be a differential operator. Differential-operator conjecture. For every PA-form $f$ on $X$, there exists a differential operator $P$ such that

$$P f\in\Omega(X).$$

This claim concerns the regularization of PA-forms by differential operators in the weak Hodge-theoretic setting of the paper; the supplied text gives no resolution of the claim.