ONE AXIOM : MATHEMATICA

One Axiom Mathematica: Coherence Valuation and Emergent Foundations from Finite Group Structure $G = S_4 \times \mathbb{Z}_2^3$ Description: This paper presents a radical re-foundation of mathematics, transitioning from the traditional axiomatic plurality of ZFC (Zermelo-Fraenkel set theory) to a single, structural foundation: the Genesis Relational Axiom (GRA). The author proves that the finite group $G = S_4 \times \mathbb{Z}_2^3$ with stabilizer $H \cong \mathbb{Z}_3$ induces a natural coherence valuation $\heartsuit$ on the coset space $G/H$. Using the geometry of the associated Schreier graph, the work derives an exponential decay of mathematical coherence ($\eta = 63/64$), leading to the discovery of…