MetaTime v36.1: Non-Markovian Cosmological Dynamics from Processing-Driven Dark-Sector Exchange Memory-Kernel Upgrade of a Kill-Test Compatible PPF-IDE Closure with Hysteresis Falsifiers

MetaTime v36.0 (RC) introduced a conservative interacting-dark-sector closure, Q ≡ 3H β_eff(a)ρ_L, and supplied a PPF-style large-scale harness to guarantee numerical stability for CMB- and growth-level tests. However, the operational map is Markovian: the interaction responds instantaneously to the local value of the proxy. Here we promote the closure to a genuinely non-Markovian (history-dependent) dynamics by replacing the algebraic schedule with a causal memory kernel over cosmic history. We introduce a latent state variable m(ln a) and adopt the minimal implementable kernel (exponential relaxation). We derive solver-ready background and linear-perturbation equations in synchronous gauge, and expand the…