Xu's conjecture on the bound for the recursively defined polynomial $T_d$

For $d\ge 3$, let $T_d$ be the recursively defined polynomial in the elementary symmetric functions on the standard simplex $T^d$, and write $\|T_d\|_{C(T^d)}$ for its uniform norm. The theorem in the paper proves the relevant least-deviation equalities for $d=3,4,5$. Xu's $T_d$ norm conjecture. For $d\ge 6$, one has

$$\|T_d(x)\|_{C(T^d)}\le 1.$$

Consequently, the equality in the two preceding least-deviation theorems also holds for $d\ge 6$. The claim is presented as the missing step in extending the proved cases to higher dimensions, and the source gives no proof for $d\ge 6$.