Conjecture on maximum divergence from trapezoid models

Let $\T_{a,b,d}$ be the trapezoid model in the simplex described above, with parameters $a$, $b$, and $d$, and let $D(\T_{a,b,d})$ denote its maximum divergence. Trapezoid-model divergence conjecture. The divergence from the trapezoid model $\T_{a,b,d}$ is at least $(a+b-1)\log 2$ and at most $(a+bd+b-1)\log 2$. This upper bound is sharp if and only if $d=0$. The preceding theorem gives a related upper bound, while the conjecture compares the trapezoid model with the two surrounding box models; the stated sharpness condition remains to be established.