MetaTime v36.5: Non-Markovian Cosmological Dynamics from Future-Latency Dark-Sector Exchange Minimal Bridge from Ontology to Effective Closure and a New Expansion-Growth Hysteresis Observable

MetaTime v36.5: Non-Markovian Cosmological Dynamics from Future-Latency Dark-Sector Exchange This version develops the MetaTime non-Markovian cosmology program by combining the original processing-driven dark-sector exchange framework with an explicit future-latency interpretation of the latent sector and a new observational discriminant. The model preserves the core technical structure introduced in earlier versions: a conservative interacting dark-sector system, a latent memory variable, a retarded kernel motivated by an open-EFT perspective, controlled perturbations, and a large-scale PPF closure. In this framework, the latent density is interpreted as a gravitationally active reservoir of compressed future states not yet executed into observable physical reality. Under this reading, the dark-sector exchange term acquires the meaning of an effective future-to-present execution flow, while the internal memory variable encodes the retarded persistence of locally available future information. The main addition in v36.5 is the introduction of a new observable signature: cosmological hysteresis in the expansion-growth plane. Because the dark sector carries memory, the relation between the expansion history and the growth history is no longer strictly single-valued. Two cosmic histories with similar instantaneous expansion rates can, in principle, produce different values of growth observables such as f sigma 8. This motivates a finite hysteresis loop in the plane defined by H and f sigma 8 as a falsifiable signature of the model. The manuscript also includes benchmark plots, certification logic, and a first pilot comparison against real H(z) and growth-rate data. In that preliminary test, the model remains competitive with LambdaCDM at the level of simple chi-squared comparison, while the best-fit region lies close to the Markovian limit, indicating that currently available H(z) plus f sigma 8 data do not yet require strong memory effects. The result is therefore both encouraging and disciplined: the framework is not ruled out by these late-time data, but its genuinely non-Markovian regime remains to be tested more strongly with fuller likelihood analyses. This version should be read as a more mature and falsifiable release of the MetaTime cosmology program, linking dark-sector memory, future latency, and late-time observables within a single effective cosmological framework.