MetaTime Kernel-Cosmology I: A Minimal Two-Layer Non-Markovian Closure with an Internal Processing Variable

This preprint presents MetaTime Kernel-Cosmology I, a minimal two-layer non-Markovian cosmological closure inspired by the broader MetaTime framework. The model organizes late-time physics into an explicit sector and a latent sector connected by bidirectional exchange. The latent-to-explicit channel is regulated by a memory variable, while the explicit-to-latent return channel is controlled by an internal processing variable.The paper extends earlier one-way memory closures developed in the MetaTime v36.x line by introducing explicit-latent circulation. In a flat FLRW background, the model is reduced to an autonomous three-dimensional dynamical system involving the explicit-sector fraction, the memory variable, and the internal processing variable. Mixed fixed points are derived, the Jacobian matrix is computed, and the associated stability conditions are discussed using the Routh-Hurwitz criteria.The main structural result is that the saddle-point obstruction found in simpler one-way autonomous reductions is removed once bidirectional exchange and internal processing are included. An illustrative parameter choice admits a stable intermediate mixed state close to one third of the explicit-sector fraction. A numerical check confirms that all eigenvalues are negative, although one eigenvalue is very small, implying slow relaxation and possible phenomenological fragility.This manuscript does not claim observational viability, does not fit cosmological data, and does not yet include perturbations or a Boltzmann-solver implementation. Its purpose is narrower: to show that a two-layer MetaTime-inspired cosmology can support stable mixed regimes once explicit-to-latent return and internal processing are included.