Kitt ideal equality conjecture for algebraic residual intersections

Let $R$ be a Cohen–Macaulay ring, let $\mathfrak a\subseteq I$ be ideals, and write

$$J=\mathfrak a:I.$$

Assume that $J$ is an algebraic $s$-residual intersection. The Kitt ideal $\operatorname{Kitt}(\mathfrak a,I)$ is the ideal constructed from the Koszul data of the inclusion $\mathfrak a\subseteq I$. Kitt ideal equality conjecture. Then

$$\operatorname{Kitt}(\mathfrak a,I)=\mathfrak a:I.$$

The claim is presented as a guess that sliding-depth hypotheses might be unnecessary for equality, although such hypotheses remain necessary in the cited context for Cohen–Macaulayness of residual intersections. The supplied text gives no resolution of this claim.