ONE AXIOM: COSMOLOGY

ONE AXIOM COSMOLOGY: Geometric Derivation of $\Lambda$CDM Parameters from Primordial Symmetry $G=S_{D+1} \times \mathbb{Z}_2^D$ (Version 2.5 Final) Description This document (2A) represents the final, reviewer-enhanced version of the cosmological analysis within the ONE AXIOM framework. It translates the Axiom-Proven geometric constants from the foundation documents (0A, 1A) into the domain of $\Lambda$CDM cosmology. The work rigorously derives key cosmological observables from a single primordial symmetry group $G=S_{4} \times \mathbb{Z}_{2}^{3}$, leveraging the Dual-Track Methodology (Optimal Coherent Representation / Optimal Epistemic Resolution) and geometric principles (Information Geometry, Berry Phase, Tsallis Entropy). Principal Results (Axiom-Proven Geometry): Dark Matter to Baryon Ratio ($\mathbf{\Omega_{DM}/\Omega_b}$): Rigorously proven ratio $\frac{\Omega_{DM}}{\Omega_{b}}=\frac{96}{S-1} \approx 5.430$, achieving 0.78% accuracy against observed data. The term $S-1$ is formally justified via the subtraction of the $\mathbb{Z}_2^3$ group ground state. Dark Energy Density ($\mathbf{\rho_{\Lambda}}$): Geometrically derived formula $\rho_{\Lambda} = \rho_{P} \exp(-S \cdot 197/13)$, achieving 1.1% accuracy. This result structurally unifies Dark Energy with the Standard Model's electro-weak sector (via the denominator 13). Baryon Asymmetry ($\mathbf{\eta_B}$): Derived value $\eta_B \approx 6.07 \times 10^{-10}$ with 0.5% accuracy, established via a formal geometric Berry Phase mechanism for CP-violation, fulfilling Sakharov conditions solely through symmetry breaking. Rigor & Consistency: This Version 2.5 includes a comprehensive Error Analysis and Uncertainty Propagation section, which demonstrates the internal consistency of the framework and directly addresses external review feedback. The high precision of the results is shown to be required by the geometric structure. The document serves as a complete, non-field-theoretic, axiomatic derivation for the greatest puzzles in modern cosmology. Keywords Geometric Cosmology, $\Lambda$CDM, Dark Energy, Dark Matter, Baryogenesis, Information Geometry, $\mathbb{Z}_2^3$ Symmetry, Tsallis Entropy, Cosmological Constant Problem, Axiomatic Physics.