Hidden-Sector Topological Dark Matter in OFGFT

Abstract We develop the hidden-sector dark-matter hypothesis formulated in Addendum IV of One Fundamental Geometric Field Theory (OFGFT) into a separate mathematical analysis. The hidden fields U’ in SU(2) and p’ are postulated to obey a Skyrme–Dilaton action with a distinct scale F’ and no direct electromagnetic, weak, or Higgs portal. We prove, conditional on admissible smooth finite-energy configurations, conservation of integer hidden winding B’ and an inversion symmetry pairing B’ and -B’ at equal classical energy. When the dimensionless hidden parameters coincide with those of the parent model, all dimensionless radial equations are inherited and the approximate mass scales as M’ = 8.10963556 F’. We display the stress-energy coupling to a shared metric and distinguish vanishing direct photon vertices from possible gravitational lensing. Analytic dimensional scaling is derived for interaction lengths, cross sections, and relic-density requirements. No new hidden-sector soliton-existence certificate, time-dependent collision simulation, thermal freeze-out calculation, or structure-formation constraint is supplied. The candidate interpretation therefore remains a physical hypothesis, while its internal symmetry and scaling relations follow from the stated action.