Uniform bound conjecture for Racah polynomials

Let $T$ be a positive integer and define the Racah polynomial

$$R_n(s,T)=R_n(s(s+1);0,0,T,-T).$$

Here $R_n(s,T)$ is symmetric in $n$ and $s$. Uniform Racah bound conjecture. For any integers $n,s$ with $0\leq n,s\leq T-1$,

$$|R_n(s,T)|\leq 1.$$

The bound would imply that the arithmetic Hodge index inequality is independent of the relative sizes of the harmonic numbers involved. The source gives no proof or resolution of this stronger assertion; it proves the needed inequality only for concave increasing sequences.