Nuttall's bounded-spurious-poles conjecture for algebraic functions

Let $f$ be an algebraic function analytic at $\infty$, and let $[n/n]$ denote its diagonal Padé approximants. A spurious pole is a pole of a Padé approximant in the sense defined in the source, with its multiplicity counted toward the total order. Nuttall's conjecture. There exists an upper bound for the total order of the spurious poles of all diagonal Padé approximants $[n/n]$, $n\in\mathbb N$. The conjecture concerns the asymptotic distribution of spurious poles and would help clarify whether Padé convergence assertions can hold for classes of algebraic functions. Its resolution status is not established by the supplied text.