MetaTime Kernel-Cosmology II: Threshold-Activated Return, Localized Processing Sources, and Fast Explicit-Latent Regulation

This preprint presents MetaTime Kernel-Cosmology II, a follow-up to MetaTime Kernel-Cosmology I. The first paper showed that a two-layer non-Markovian cosmological closure with an explicit sector, a latent sector, a memory variable, an internal processing variable, and bidirectional exchange can admit stable mixed fixed points, but that the simplest linear return law leads to very slow relaxation. The present work shows that this slow direction is not a structural obstruction of the MetaTime kernel. Instead, it arises from the choice of a linear explicit-to-latent return law. By replacing the linear return channel with a threshold-activated nonlinear return function, the slow eigenvalue can be lifted by more than an order of magnitude. For a conservative sigmoid return with exponent n = 4 and moderate amplitude, the slow eigenvalue improves from approximately -0.034 to approximately -0.36, while the persistent one-percent relaxation time decreases from roughly 115 e-folds to about 14 e-folds. A sweep over the threshold scale shows that acceleration is not limited to a single tuned value: significant fast regulation persists across an asymmetric threshold window spanning roughly a factor of six. The paper also identifies two acceleration regimes. Near the operating scale, regulation is threshold-dominated and controlled by the local slope of the nonlinear return function. Below the operating scale, regulation becomes saturation-dominated because the return channel is already substantially active. Sharper nonlinearities can accelerate relaxation further, but they may introduce damped oscillatory eigenmodes. This manuscript is restricted to background-level dynamical systems. It does not claim observational viability, does not fit cosmological data, and does not include perturbations or a Boltzmann-solver implementation. Its purpose is to establish a structural result: nonlinear threshold-activated return can convert merely stable explicit-latent circulation into fast regulation over a finite threshold window.