Kresch–Tamvakis conjecture for a terminating hypergeometric series

For any positive integer $D$ and integers $i,j$ satisfying $0\leq i,j\leq D$, define the Pochhammer symbol by $(a)_n=a(a+1)\cdots(a+n-1)$ and the hypergeometric series

$${}_4F_3\left[\begin{array}{c}a_1,a_2,a_3,a_4\\ b_1,b_2,b_3\end{array};z\right]=\sum_{n=0}^{\infty}\frac{(a_1)_n(a_2)_n(a_3)_n(a_4)_n}{(b_1)_n(b_2)_n(b_3)_n}\frac{z^n}{n!}.$$

Kresch–Tamvakis conjecture. The following terminating hypergeometric series has absolute value at most $1$:

$$\left|{}_4F_3\left[\begin{array}{c}-i,\ i+1,\ -j,\ j+1\\1,\ D+2,\ -D\end{array};1\right]\right|\leq 1.$$

The conjecture was posed by Kresch and Tamvakis in 2001 and is resolved by the paper containing this statement; the provided text does not specify the proof's status beyond asserting that the conjecture is proved.