Part IV of the RLDS series. This paper develops three structural cosmological consequences of the RLDS dark-sector attractor. First, it shows that cosmic acceleration becomes a geometric consequence of the attractor structure rather than a coincidence of initial conditions. Second, under exact shooting self-consistency, the present-day matter density becomes a derived output of the ODE instead of a free input parameter. Third, within the benchmark RLDS closure studied here, self-consistent solutions require phantom dark energy, that is, w < -1. The paper also establishes an H-theorem through a Lyapunov functional, derives the covariant Q-law associated with the RLDS flow, and formulates a falsification program for future observational tests. The theorem-level statements and the benchmark numerical results are explicitly distinguished. Paper I: singular-attractor prototype mathematics. Paper II: canonical RLDS framework and reduction criteria. Paper III: paired observational signature. Paper IV (this work): cosmological consequences under RLDS closure. Paper V: representative microphysical descent to RLDS.
Aleksander Kubanski (Mon,) studied this question.