ONE AXIOM : ABC: Alignment-Based Coherence

ABC: Alignment-Based Coherence – From Primordial Quartet to Dimensional Emergence (Version 1.0) Abstract: This document establishes the mathematical foundations for the $\pi_5$ layer, a ontological pre-physical level of structure that precedes physical manifestation. Using the "Alignment-Based Coherence" (ABC) framework, the work demonstrates how a fundamental quartet of elements $\{0, \heartsuit, \mathfrak{F}, 1\}$ gives rise to the symmetry group $G = S_4 \times \mathbb{Z}_2^3$. The treatise employs a rigorous Dual-Track (Cyclic-Binary Convergence) methodology to identify the structural constraints that govern this layer. Key achievements include: Mathematical Necessity of 4-Fold Structure: A formal…