Sub‑Leading Terms The Predictive Power of Quantum Noise A Geometric Approach to Catastrophic Failure Prediction

In the arithmetic geometry of Shimura varieties, Ryan Chen has recently demonstrated that at near‑center points of functional symmetry, both the leading special value (complex volumes) and the subleading first derivative (arithmetic volume) simultaneously carry geometric meaning. This paper establishes a direct physical analog of this profound mathematical phenomenon. Using the GeoUnify 52D geometric framework, we show that in composite quantum systems (QEC stacks, qubit arrays), the ``noise''—traditionally discarded as random fluctuation—encodes predictive information about impending catastrophic failures. We define sub‑leading geometric invariants derived from second‑order statistics of the Geometric Stability Score (GSS) and demonstrate that they function as near‑center derivatives of an empirical L-function associated with system stability. Numerical experiments on error correction stacks show that these invariants detect failure precursors with 200‑step anticipation, outperforming traditional metrics by orders of magnitude. This work establishes a rigorous bridge between arithmetic duality and quantum system engineering, introducing the concept of antifragile design: systems that learn from small perturbations to prevent catastrophic collapse.