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 numerical certification suite to include a strict "Hysteresis Test" (path-dependence falsifier). By adopting a non-Markovian lens, this upgrade moves the framework from a time-varying coupling prescription to a structural model where dark-sector exchange possesses an internal clock and memory. Version Notes (v36.1 vs v36.0 RC) Transitioned from a Markovian interaction map to a causal memory kernel (non-Markovian dynamics). Introduced a formal Hysteresis/Path-dependence kill-test to the certification suite. Companion Framework This cosmological formulation shares its mathematical architecture (retarded response and information inertia) with the cognitive sector of the framework. See the companion paper: MetaTime v36.5.3: TableMacro Discipline and Non-Markovian Anchoring in the Universal Law of Consciousness.