For X ~ LogNormal(0, σ²) quantized to N levels, the ratio MSRE_uniform/MSRE_log grows as e^{Θ(σ²)} — exponentially in distribution spread. At σ=2 the ratio exceeds 346,000×; at σ=3 it exceeds 17 trillion×. Under MSE the two quantizers are comparable (ratio ≈ 1). Lean 4 verified.
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