Polynomial bound for symbolic-power generators in general

Establish whether, for every Noetherian local ring R and ideal I contained in R, the sequence of minimal numbers of generators {μ(I^(n))} is bounded above by a polynomial in n.

Background

The paper introduces the symbolic analytic spread of an ideal I as the infimum of exponents governing polynomial growth of μ(I^n). Before stating the first main theorem, it identifies the general polynomial-growth question for symbolic powers as unresolved. The theorem proved in the paper establishes finiteness of the symbolic analytic spread when R is essentially of finite type over a field, so the broader question for arbitrary Noetherian local rings remains outside the proved scope.