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Variable-Cliff Nielsen Geometry and an Exponent -4/3 Lower Bound for the Infinite-Cliff Diameter
Let $D=2^n$ and $M=3n+9\binom n2$. We study the right-invariant one-step-cliff metric $d_Q$ on $\operatorname{PU}(D)$, with unit penalty on Pauli weights one and two and penalty $Q$ on all higher weights. If $M/Q_D\to0$ and $MQ_D^{3/4}/D^2\to0$, then, for every fixed $0<x<π/\sqrt3$, \[ μ_D\bigl(B_
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