The Spectrum of a Compact Internal Space II: Effective Couplings and Mass Scales

Abstract

Minimal unbiased compositional change generates the Gaussian source of the compact internal construction. We derive joint constraints on effective couplings and mass scales from its gauge and matter content, scalar sector, spectral endpoint and kinetic normalizations. Compatibility of source and colour screening selects three matter copies. Within the response family indexed by integers, shell support and position retention select the level R=5, whose transverse traceless endpoint equation has a unique positive root. Eliminating shared transfer parameters gives a relation among six geometric fermion masses. Bandwidth variation correlates the electron and electroweak scales, while two cosmological ratios are independent of the common neutrino mass normalization. Finite matching through one loop implements the generated Fermi, top and Higgs conditions in a common action. The absorptive top self energy gives the Born decay width as an additional output. The compact source covariance and positive RMS amplitude determine a local nonlinear flux that couples matter motion to source feedback. A model with an auxiliary radius admits autonomous source evolution, positive reduced propagation forms and a matter phase clock on a specified finite cosmological interval. Physical comparisons use the stated mass definitions, matching and thermal approximations. The fixed DESI DR2 distance comparison gives \c{hi}^2 = 29.5087 for thirteen components and p=0.00554, indicating tension in the adopted cosmological mapping. Spectral tail and quadrature bounds control the finite response calculation.

arXiv comment166 pages, 0 figures. Numerical code is included as an ancillary file. All scientific content, derivations, and conclusions are solely the work of the authors