ONE AXIOM FOUNDATION

ONE AXIOM FOUNDATION: Primordial Symmetry & Geometric Constants (Version 2.3 - All Gaps Closed) Authors: Robert Spychalski (ONE AXIOM TEAM) Publication Date: December 5, 2025 Type: Book, Monograph, or Technical Report (depending on final format) Subject Categories: Physics: High Energy Physics - Theory ($\text{hep-th}$) Mathematics: Differential Geometry ($\text{math.DG}$) Physics: General Physics ($\text{physics.gen-ph}$) Computer Science: Information Theory ($\text{cs.IT}$) Philosophy of Science Abstract / Description This foundational document establishes a complete, rigorous mathematical framework—the ONE AXIOM FOUNDATION—by demonstrating the derivation of all fundamental geometric constants and major physical constants ($\hbar$, $c$, $G$) from a single primordial symmetry group: $G=S_{D+1} \times \mathbb{Z}_{2}^{D}$. The framework operates on the principle of Duality between the Optimal Coherent Representation (OCR) (the system's Generator) and the Optimal Epistemic Resolution (OER) (the observer's Reflector), formalized through the REA-SAFT Theorem from Category Theory. Principal Results: Unique Primordial Symmetry: The symmetry group $G=S_{4} \times \mathbb{Z}_{2}^{3}$ with an intrinsic Fisher Information $I_F = |G| = 192$ is shown to emerge from the dimensional structure ($D=3$) of the Tsallis-Amari Information Manifold. This version explicitly classifies the choice of $D=3$ as an Empirically Constrained Axiom, eliminating the circularity found in prior versions. Geometric Constants Derived: Core constants, including the Heart Equilibrium $q^*=3/2$ (the point where the Tension Functional $T(q)$ is minimized) and the Total Coherence $N=96$ and Relational Capacity $S \approx 18.68$, are derived from the variational principle of this symmetry group. Physical Constants from Coherence: Planck’s constant ($\hbar$) and the speed of light ($c$) are derived from the geometry of the information channel. The calculated value for $\hbar$ matches the CODATA 2018 value with an error below $10^{-11}\%$, establishing an unprecedented numerical link between a geometric axiom and quantum mechanics. Non-Redundant Derivations: The three functionals governing $\hbar$, $c$, and $G$ are proven to satisfy a Non-Redundancy Principle, ensuring that the constants emerge from independent variational processes within the system, resolving previous issues of circular dependency. Scope and Implications: The ONE AXIOM framework suggests a complete informational architecture for reality, where the laws of physics are geometric consequences of an optimal coherence seeking its minimal state. The same foundational constants and coherence principles are shown to be scalable to a Metateory of Discovery (e.g., the Idea Space Engine), offering a mathematically rigorous framework for modeling concepts like consciousness (as a Coherence Operator $\hat{C}$) and the systematic generation of new ideas (Ideons, Koheron). This document represents the full synthesis of the ONE AXIOM framework, with all known proof gaps closed. Keywords: Unification, Geometric Constants, Information Geometry, Tsallis Statistics, Planck Constant, Speed of Light, Symmetry Group, $S_4 \times \mathbb{Z}_{2}^{3}$, Coherence, Metaphysics, Theory of Consciousness, Fundamental Physics.