Bounded roots conjecture for eigenpolynomials of exactly solvable operators

Consider a fixed order-$k$ linear ordinary differential operator family with monic polynomial leading coefficient $Q_k(z)$ of degree $k$. An operator is exactly solvable if its coefficient polynomials satisfy $\deg Q_j\leq j$ for $j=1,\dots,k$, with equality for at least one $j$, and a sequence of such operators has moderate growth if, for each $j=1,\dots,k-1$, the coefficients of $Q_{j,n}(z)/n^{k-j}$ remain bounded. Bounded roots conjecture. For any sequence $\{\mathfrak d_n(z)\}$ of exactly solvable operators of moderate growth, the union of all roots of all their eigenpolynomials is bounded in $\mathbb C$. This conjecture asserts global root boundedness for eigenpolynomials arising from moderately growing exactly solvable operators; the paper presents it as a general conjecture supported by evidence, with no resolution stated in the source.