Ce Shen
For an untwisted Wess--Zumino--Witten modular tensor category $\cC(\mathfrak g,k)$, let $r(\mathfrak g,k)$ be the number of simple objects and $\cD(\mathfrak g,k)$ its total quantum dimension. The vacuum-flux state on a torus divided into two cylinders has positive universal entropy contribution $Γ_{T^2}=2\log\cD$. We maximize this quantity over all simple Lie algebras and positive integral levels subject to $r(\mathfrak g,k)\leq R$. If $q_R=\log_2R$, then $Γ_{\max}(R)\sim[7ζ(3)/(4π^2)]q_R^2$ as $R\to\infty$. The sequence $Sp(2n)_n$ attains the asymptotic coefficient. At equal rank and level, the Fourier expansion of the type-$C$ root product loses its even modes, leaving $2π^{-2}\sum_{m\,\mathrm{odd}}m^{-3}=7ζ(3)/(4π^2)$. An entropy--spectral inequality proves optimality among the classical families, while rank--level duality and fixed-rank estimates control unbalanced and exceptional sequences.