Dimension bound for symbolic analytic spread

Determine whether the symbolic analytic spread sell(I) is always at most the Krull dimension dim(R) for every ideal I in the relevant Noetherian ring R.

Background

After proving that the symbolic analytic spread is finite for rings essentially of finite type over a field, the paper asks for effective bounds on this invariant. In particular, it highlights the proposed upper bound sell(I) ≤ dim(R), cited as a conjecture in earlier work. The paper does not resolve this bound; its main theorem supplies finiteness but not the stated dimension-dependent estimate.