A uniform bound for the correction term in integer matrix enumeration

Let $m,s,n,t$ be positive integers satisfying $ms=nt$. Let $M(m,s;n,t)$ denote the number of $m\times n$ matrices of nonnegative integers with every row sum equal to $s$ and every column sum equal to $t$, and let $G(m,s;n,t)$ be the asymptotic main term defined in the paper. Define $\Delta(m,s;n,t)$ by

$$M(m,s;n,t)=G(m,s;n,t)\Bigl(\frac{m+1}{m}\Bigr)^{(m-1)/2}\Bigl(\frac{n+1}{n}\Bigr)^{(n-1)/2}\exp\Bigl(-\frac12+\frac{\Delta(m,s;n,t)}{m+n}\Bigr).$$

Bounded-correction conjecture. For every such 4-tuple,

$$0<\Delta(m,s;n,t)<2.$$

This conjecture gives a uniform bound on the correction term in the asymptotic formula for the number of nonnegative integer matrices with prescribed constant row and column sums. The supplied text presents it as a conjecture suggested by exact computations; no resolution is given in the source context.