The JGunicox Conjecture Unifying Geometric Stability and Spectral Variables in Quantum Systems

This consolidated work presents a comprehensive geometric framework for understanding stability and predictability in quantum systems. The Geometric Stability Score (GSS) — a measure derived from a 52‑dimensional isometric embedding of quantum state space — is shown to obey a universal linear relation with spectral variables across five fundamental systems. This relation, termed the transformation, achieves R²>0. 88 and enables proactive decoherence prediction. Rigorous definitions of the 52‑dimensional manifold, geometric fractures, and early‑warning metrics are provided, supported by extensive numerical validation. The cumulative evidence leads to the JGunicox conjecture, which posits a universal geometric‑spectral duality underlying quantum stability. The work establishes GeoUnify as a computational bridge between quantum engineering and deep mathematical ideas, with implications for proactive error correction.