The Geometric Origin of Cosmological Tensions: Unifying Gravity, Electromagnetism, and Matter Generations via Flux Compactification

Version 2: Refined mathematical derivation using canonical normalization of the scalar modulus. Clarified the relationship between flux parameters (λ_th vs λ_obs) and topological constraints. Introduced effective gauge coupling ν_eff ≈ 0.633 from D-brane geometric projection, resolving inconsistencies in v1. Minor updates to references and consistency checks. We propose a unified geometric framework that resolves the Hubble Tension (H0) and explains theanomalous abundance of early massive galaxies observed by JWST, while simultaneously derivingthe number of fermion generations. By imposing a dynamic energy balance between the kineticterm of a scalar modulus and its flux-induced potential, we derive a universal scaling coefficient n ≈0.2672. This coefficient governs the evolution of effective physical constants in the early Universe. Wedemonstrate that this value is not arbitrary but arises from the topology of a Calabi-Yau manifoldwith Hodge number h1,1 = 3. This specific topology enforces a “Trinification” of the gauge group(E6 → SU (3)3), naturally resulting in exactly three generations of matter (Ngen = 3). The modelpredicts a specific violation of the distance-duality relation, testable by future gravitational waveobservatories.