For an untwisted Wess--Zumino--Witten modular tensor category ( g,k), let r(g,k) be the number of simple objects and ( g,k) its total quantum dimension. The vacuum-flux state on a torus divided into two cylinders has positive universal entropy contribution Γ_T²=2. We maximize this quantity over all simple Lie algebras and positive integral levels subject to r(g,k)≤R. If qR=log2R
Nearby in the stack
, then
Γmax(R)∼[7ζ(3)/(4π2)]qR2
as
R→∞
. 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∑moddm−3=7ζ(3)/(4π2)
. An entropy--spectral inequality proves optimality among the classical families, while rank--level duality and fixed-rank estimates control unbalanced and exceptional sequences.
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