Fourier-support-aware Weyl normalization

Use this in a phase-space convolution, neural operator, or learned Weyl layer whose parameters define a symbol a. The integration point is immediately before applying the layer to activations: compute a discrete symplectic Fourier transform of the symbol parameters, estimate their frequency radius, multiply the layer output by the normalization factor, and then apply any residual connection. On a discrete two-dimensional phase-space grid, let u_j denote sampled symbol coefficients and z_j their phase-space frequency coordinates. Compute weights w_j = |F_sigma u_j|^q, then calculate R_eff = max(1, sqrt(sum_j ||z_j||^2 w_j / (sum_j w_j + delta))). Set alpha = (2d + 1 + epsilon_exp) abs(1 - 2/p) and scale = R_eff^(-alpha). The forward computation is: a = weyl_apply(symbol, x); y = scale times a. Initially stop gradients through R_eff to prevent the normalization estimator from creating unstable feedback. The paper supplies the support-dependent exponent and the special role of p = 2; the effective-radius estimator is an empirical replacement for exact compact support. Compare hard support radius, percentile radius, and the displayed second-moment estimator. First test on CIFAR-10 or a 64 by 64 image-regression task with a learned Fourier or Weyl layer. Compare no normalization and standard weight normalization at several resolutions. Track gradient-norm variance, estimated largest singular value, validation error, and convergence at equal FLOPs. Success means resolution-invariant activation gain and fewer unstable runs without accuracy loss.