MetaTime v36.2: Non-Markovian Cosmological Dynamics from Processing-Driven Dark-Sector Exchange Physically Anchored Memory, Controlled Perturbations, and Illustrative Observable Benchmarks

MetaTime v36.2 is a revised and strengthened version of the v36.1 non-Markovian cosmology framework. The manuscript develops a memory-kernel upgrade of the MetaTime interacting dark-sector closure, replacing the instantaneous Markovian schedule of v36.0 with a causal latent state that evolves through an exponential relaxation kernel. This promotes the dark-sector exchange from a purely local prescription to a structurally non-Markovian model with an internal response timescale. Compared with v36.1, this version removes the central dependence on private communication, derives the memory-kernel motivation directly from the Schwinger-Keldysh / Feynman-Vernon open-EFT viewpoint, anchors the relaxation-width parameter Delta to an effective physical timescale, and presents the EFT embedding more conservatively as a consistency template rather than a fully specified ultraviolet completion. The treatment of perturbations is also clarified by making explicit the minimal approximation for the proxy perturbation and its controlled extension. This version additionally includes benchmark observable figures and qualitative discriminants for H(z), a quasi-GR proxy for f sigma_8(z), the evolution of the effective coupling beta_eff(z), and a hysteresis illustration showing path dependence at fixed present proxy value. The result is a more submission-ready preprint: still conservative and solver-oriented, but now more explicit about its physical motivation, parameter interpretation, and observational signatures.