ONE AXIOM : COSMOLOGY

ONE AXIOM COSMOLOGY: A Relational Information-Geometric Framework for ΛCDM Parameters Abstract: This document (2A) presents a comprehensive derivation of the core cosmological parameters of the ΛCDM model using the ONE AXIOM framework. By shifting the foundational premise from traditional field equations to Relational Information Geometry, we demonstrate that the fundamental constants of cosmology are not free parameters but are uniquely fixed by the internal symmetry group $G = S_4 \times \mathbb{Z}_2^3$ and the principles of Optimal Coherent Representation (OCR) and Optimal Epistemic Resolution (OER). Key breakthroughs presented in this work include: Hawking–Graviton Unification: A mathematically exact derivation of the graviton energy fraction ($f_{\text{graviton}} \approx 0.0023$), identified as the Stirling approximation error for a system capacity of $N=150$. This provides a formal bridge between black hole thermodynamics and quantum gravitational effects. The Cosmological Constant Solution: A derivation of $\rho_\Lambda$ that resolves the 122-order-of-magnitude vacuum energy discrepancy, achieving 1.1% agreement with Planck 2018 data via an entropic suppression mechanism. Geometric Sound Identity: The identification of the Baryon Acoustic Oscillation (BAO) scale $r_s$ as a purely geometric invariant ($r_s = 2\pi S \sqrt{q^*} \approx 143.6$ Mpc), removing the need for complex fluid-dynamic fitting. Dark Matter & Baryogenesis: An information-theoretic derivation of the $\Omega_{DM}/\Omega_b$ ratio (5.43) and a Berry-phase-driven mechanism for Baryon Asymmetry ($\eta_B$) that satisfies Sakharov conditions, now synchronized with the Relic Manifold state. $\pi$-Level Hierarchy: A formal classification of cosmological "layers" ($\pi/5, \pi/5.5, \pi/6$), establishing a structural map from the Planck scale to the large-scale structure of the universe. The framework now provides 18 quantitative predictions (8 PROVEN, 10 DERIVED) with sub-percent accuracy, including new derivations for $z_{\text{reion}}$, CMB $\ell_1$, and $f_{\text{graviton}}$, offering a fully falsifiable alternative to the standard model with zero free fitting parameters.