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Z. Zhang
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Finite-time blow-up is proven for supercritical defocusing nonlinear wave equations in $d\geq4$ by rigorously verifying analytic radius conditions and controlling cumulative growth via frequency-dependent multipliers.
Pixel diffusion’s chronic high-frequency blur is not an architectural bottleneck: a lightweight adversarial post-training phase restores natural spectral power laws without causing mode collapse or requiring changes to the sampling pipeline.