Spectral-Abscissa Early-Warning Scheduler

Add a monitoring callback to the training loop. Every M=10-50 optimizer steps, record a minibatch-loss residual after subtracting an exponential moving average, the global gradient norm, and one or more fixed random projections of the parameter update. On a rolling window of N=100-500 samples, compute variance and lag-one autocorrelation, then estimate the recovery rate as r_hat=-log(rho_1)/Delta t. Smooth each statistic with an exponential moving average and compare it with the median during the first 20% of training or with a no-delay control run. When rho_1 rises by 0.1-0.2, variance doubles, or r_hat falls below a fixed fraction of baseline, apply eta <- 0.5 eta and beta <- min(beta,0.9); restore hyperparameters only after r_hat recovers. The AR(1) relation and variance law are paper-derived; rho_1, variance, and r_hat are estimated empirically. First test on a small Transformer or ResNet with artificially stale gradients and compare fixed hyperparameters against this scheduler. The predicted signature is critical slowing down before divergence: rho_1 should increase toward one, variance should scale approximately as 1/(1-rho_1^2), and recovery rate should approach zero. After intervention, these trends should reverse. If no pre-divergence increase appears, reject the mechanism for that optimizer or change the observable.