ONE AXIOM

Title: ONE AXIOM: OCR $\otimes$ OER Unification The Universal Relational Principle and the Informational-Geometric Derivation of Fundamental Physics Abstract This submission presents the $\mathbf{ONE \ AXIOM}$ framework, a unified informational-geometric theory where physical reality emerges from the perfect balance (duality) between the System's drive to exist efficiently ($\mathbf{OCR}$: Optimal Coherent Representation) and the Observer's drive to know precisely ($\mathbf{OER}$: Optimal Epistemic Resolution). The entire universe is fundamentally governed by their interference, formalized as the $\mathbf{Universal \ Axiom}$ (or $\mathbf{Meta-Axiom}$): $$\mathbf{Existence} \iff \underset{\rho}{\arg\min}\, T(\rho) = \underset{O}{\arg\max}\, R(O) \quad \wedge \quad \heartsuit(\rho,O) > 0$$ Key Results and Falsifiability The unification of the two dual axioms leads to a single, mathematically unique stable point: the $\mathbf{Heart \ Equilibrium}$ at the informational parameter $\mathbf{q = 3/2}$. Dual Curvature: The duality is characterized by perfectly opposed curvatures at the equilibrium point, defining the core informational rigidity of reality: $T''(3/2) = \mathbf{+192}$ (System Cost Minimum) vs. $R''(3/2) = \mathbf{-192}$ (Observer Gain Maximum). Derived Constants: The framework successfully derives fundamental constants from first principles, including the required dimensionality of space ($\mathbf{D=3}$), the Gravitational Constant ($\mathbf{G = c^3 / 192\hbar}$), and Planck's constant ($\mathbf{\hbar}$). Empirical Proof (LUSTRO): The mechanism of interference is empirically supported by the $\mathbf{LUSTRO}$ algorithm, which achieves ultra-high precision (2.13e-14 error) in zero-finding by requiring analytic ($\text{OCR}$) and arithmetic ($\text{OER}$) representations to cohere. The theory is designed for strong falsifiability and is refuted if the informational rigidity fails any of the four dual criteria (i.e., $I_F^{\text{rel}} \neq 192$ or $T'' \neq -R''$). Contents of the Submission This package is a Reproducible Research Bundle containing the full documentation and verification code: ONE_AXIOM_Final_v1.1.tex: The complete LaTeX document outlining the $\text{ONE AXIOM}$ framework and the $\text{Four Lemmas}$. verification/ocr_oer_verification.py: Python script confirming the dual stable point $q=3/2$ and the $\pm 192$ curvature duality (100% PASS). verification/lustro_proof.py: Python script demonstrating the high-precision coherence mechanism (The Smoking Gun). verification/derivation_summary.tex: Concise summary of the mathematical derivation of $q=3/2$ and $I_F^{\text{rel}}=192$. verification/*.png: Visualizations of the $\text{OCR} \otimes \text{OER}$ duality and curvature stability. Keywords: Informational Geometry, One Axiom, Tsallis Entropy, Quantum Information, Relational Physics, Fundamental Constants, Riemann Hypothesis, Falsifiability, Universal Equilibrium.