Geometric Intersection Invariants for Quantum Error Correction Stacks A Computational Approach to Arithmetic Duality

Inspired by the Gross--Zagier formula and Ryan Chen's work on arithmetic cycles in Shimura varieties, this paper introduces the concept of \textbf{geometric intersection invariants} for composite quantum systems. We define a quantitative measure of how modifications in one component impact the global stability of the entire stack. Using the GeoUnify platform, we demonstrate that these invariants can be computed numerically with 99.9999\% precision and present evidence that they satisfy relations analogous to derivatives of L-functions. This work establishes a bridge between arithmetic geometry and quantum systems engineering, opening new avenues for designing robust architectures.