Replace weak-Schatten control with multiplicative-spectrum diagnostics

Integrate this as a monitoring and regularization ablation for matrix adapters, MoE expert transformations, token mixers, or low-rank fine-tuning modules that currently use weak-Schatten or top-tail penalties. At every monitoring interval, compute sA = svdvals(A) and sB = svdvals(B), set q = sort_desc(sA[:r] * sB[:r]), and evaluate strong = (sum(q p)) (1/p), weak = max(k ** (1/p) * q[k-1] for k from 1 to r), and logprod = cumulative_sum(log(q + epsilon)). Logprod should be inspected for every k, not only at the largest singular value. Run three conditions: weak penalty lambda times weak, strong penalty lambda times strong^p, and no spectral penalty. Tune lambda separately using a small validation set, then compare at matched training loss or matched parameter norm. The paper supplies the failure mode and the diagnostics; the coefficient, epsilon, rank truncation, and monitoring interval are empirical. A cheap first experiment is a CIFAR-100 small ViT with a learned token mixer and a low-rank channel adapter. Record validation loss, gradient norms, maximum of ||A X B||_F divided by ||X||_F, and the trajectories of weak, strong, and each L_k. The hypothesis is falsified if weak and strong penalties produce indistinguishable stability and generalization across multiple seeds; support is obtained if weak-norm runs show improved W_p but worse intermediate L_k or operator amplification, while strong control avoids those events.