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The aim is to establish a mathematical framework for understanding the $C0_5$ layer's pre-physical structure.

July 1, 2026Open Access

ONE AXIOM : ABC: Alignment-Based Coherence

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The aim is to establish a mathematical framework for understanding the $C0_5$ layer's pre-physical structure.
Develops the ABC framework to explore the symmetry group $G = S_4 imes \\mathbb{Z}_2^3$.
Employs Dual-Track (Cyclic-Binary Convergence) methodology for structural analysis.
Demonstrates 136 results including 91 theorems, 36 corollaries, and 9 propositions.
Demonstrates mathematical necessity of a coherent alignment in the $S_4$ framework requiring four ontological dimensions.
Identifies the $51{:}13$ ratio of allowed to forbidden states.
Establishes density factorization identity $|\\mathcal{F}|\cdot\delta_{\mathrm{rel}} = 13/64$.

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Mathematical foundations establish alignment-based coherence in ontological dimensions, suggesting new structural insights.

Robert Spychalski (2026) studied this question.

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