Hassanzadeh–Naeliton conjecture for algebraic residual intersections

Let $R$ be a Cohen–Macaulay local ring of dimension $d$, let $I$ be an ideal satisfying sliding depth, and let $s$ be the residual-intersection parameter. An algebraic $s$-residual intersection is an ideal $J=\mathfrak a:_R I$ satisfying the algebraic residual-intersection hypotheses. A disguised residual intersection is the ideal obtained from the associated Koszul–Čech construction. Hassanzadeh–Naeliton's conjecture. If

$$\operatorname{depth}(R/I)\geq d-s,$$

then every algebraic $s$-residual intersection of $I$ coincides with the disguised residual intersection. The preceding results establish this coincidence in several cases, including height-two ideals and arithmetic residual intersections, while the supplied text leaves the stated generality unresolved.