ONE AXIOM : The Entropy-Coherence Isomorphism

Title: The Entropy-Coherence Isomorphism: Local Thermodynamic Projections from Finite Group Structure Description: Abstract: This paper, designated as Document 1B of the ONE AXIOM framework, presents a formal derivation of the five laws of thermodynamics from the structural invariants of the finite group $G = S_4 \times \mathbb{Z}_2^3$. Using a novel dual-track methodology—distinguishing between Ontological Coherence Resolution (OCR) and Ontological Epistemic Resolution (OER)—we resolve the long-standing problem of energy circularity by defining temperature and entropy as emergent projections of group-theoretic constraints. Key Technical Pillars: Entropy-Coherence Isomorphism (Theorem T8): We establish the…