This volume embeds the Transcendent Theory of R-layer Mode Theory (RLMT) into concrete cosmological models and derives observational predictions across the inflationary, large-scale structure, and gravitational-wave sectors. Building on the categorical and operator-theoretic foundations established in Volumes LXXVI–LXXVIII, we map the spectral data of the transcendent eigenobject—together with instanton norms and the universe fibration structure—to standard cosmological quantities. We obtain rigorous relations between the spectral gap and the scalar spectral tilt and running, and prove that the instanton norm at the transcendent fixed point leads to exponential suppression of primordial non-Gaussianity. In the tensor sector, we construct a decay-modified tensor spectrum predicting a naturally negative tensor tilt and high-frequency suppression, providing a characteristic RLMT signature in the LIGO/LISA/PTA bands. We further outline a global RLMT likelihood framework for joint inference from CMB, LSS, and GW data, and discuss effective field theory and information-geometric interpretations of RLMT. This volume completes the bridge from the abstract operator-algebraic and categorical structure of RLMT to concrete, testable cosmological predictions.
Tsuyoshi Tohi (Fri,) studied this question.