Foundations of the Six-Dimensional Geometric Field Theory: Deriving the Standard Model and Cosmology from Topological Axioms

The Six-Dimensional Geometric Field Theory (SDGFT) presents a novel foundational framework that bridges the discrete geometry of quantum mechanics with the continuous spacetime of general relativity. This paper demonstrates that the fundamental constants of both the Standard Model of particle physics and ΛCDM cosmology can be derived analytically without the use of free parameters. The framework is constructed upon two rigid topological axioms originating from the properties of the 4D 24-cell polytope: the lattice tension δ=1/24 (derived from the kissing number 24) and the matter asymmetry Δ=5/24 (derived from the Fibonacci resonance collision). Through multiplicative topological projections and a self-referential dimensional fixed-point attractor (D₀≈2. 7917), these inputs generate a unified scale-dependent geometry. Key Results: We present a comprehensive 57-parameter scorecard comparing SDGFT predictions against current empirical data (including PDG 2024, Planck 2020, DES-Y3, and SPARC). The framework successfully predicts: Exact analytical values for the fine-structure constant (α^−1), the Higgs mass (mH), and the Weinberg angle (sin² θW), including precise Renormalization Group (RG) running. The exact partitioning of the Universe's energy density at the Planck scale (ΩDE, ΩDM, Ωb). The dynamical running of Dark Energy and the emergence of the galactic transition scale (rₖpc≈1. 02 kpc) without requiring dark matter particles. Falsifiability: Unlike models that fit free parameters to match observations, the zero-parameter nature of SDGFT necessitates strict, falsifiable deviations from standard models. Notably, the theory predicts a dynamical Dark Energy equation of state wDE≈−0. 932, providing a clear target for upcoming observational campaigns such as the Euclid mission and CMB-S4.