The spectrum of a compact internal space. II. Effective couplings and mass scales

Abstract

This paper studies the numerical consequences of a fixed compact spectral datum, taken here to be the Laplace and Dirac spectra of RP^3, together with a specified scale-flow prescription. The structural content supported by this datum, namely the gauge algebra, the fermion representation content, and the positive colour-singlet scalar scale, is recorded in the companion paper, and the present paper evaluates its numerical consequences. The calculation closes the dimensionless window capacity and evaluates a set of effective couplings, mass ratios, and low-energy scales. After the structural datum and the closure prescriptions are fixed, no continuously adjusted phenomenological parameter is introduced in the numerical chain. The resulting quantities are compared with representative Standard Model and cosmological reference values, and the deviations are reported together with the sensitivity to the main closure choices. The deviations are central-value comparisons rather than a global statistical fit. The results are stated as scheme-conditioned consequences of the spectral construction. Several downstream applications are explicitly marked as exploratory and are not included in the core comparison. Keywords: spectral datum, compact internal space, effective couplings, scale flow, positive scalar mass, numerical evaluation