Future as Possibility, Present as Selection, Past as Active Constraint: A Minimal Causal Realization of the Cosmology of Time

What if dark energy, classical selection, and dark matter are not independent ingredients of the Universe, but three temporal regimes of a single informational process that generates physical reality itself? In the broader Cosmology of Time (CT), the Future (Dark Energy) is proposed as the domain of open possibilities, the Present (classical selection) as the domain of physical actualization, and the Past (Dark Matter) as the accumulated regime of sedimented records that can actively constrain what happens next. In its full cosmological form, this triadic grammar is associated with the large-scale structure of reality: Future as possibility, Present as actualization, and Past as historical constraint. This work does not yet test the cosmological model directly. Instead, it presents a minimal causal realization of its underlying grammar. Using a collision model with memory, this toy program asks whether the core internal logic of the CT framework can be instantiated in a minimal, explicit, and computationally inspectable system. The result is a formal exercise in which: the Future appears as accessible possibility space, the Present appears as selection plus recording, the Past appears as sedimented record, and accumulated memory acts back on the system as an active constraint on subsequent evolution. The model also isolates a nontrivial distinction between decoherence and registration, and exhibits a measurable compression of accessible future under historical accumulation. Most importantly, the program succeeds in showing that the internal grammar of the CT framework admits a coherent minimal causal realization: Future, Present, Past, sedimented record, and active memory can all be instantiated within a single causal architecture, while the separation between decoherence and registration and the historical compression of accessible future emerge as nontrivial formal results. This is not yet a predictive cosmological theory. It is the first minimal formal test of whether the internal grammar of the Cosmology of Time can be realized as a coherent causal program. The deposit includes the main preprint, supplementary technical documentation, and a code appendix with the available source implementations.