Hermitian Spectral Bounds as Real-Time Feasibility Diagnostics

Modern control and learning-enabled systems increasingly operate in regimes where classical global guarantees are either unavailable or impractical to enforce in real time. This work introduces a feasibility-based control-geometric framework centered on Hermitian Spectral Bounds (HSB), designed to act as real-time diagnostics for stability preservation under model uncertainty, learning dynamics, and structural deformation. Rather than enforcing global optimality or asymptotic stability, the proposed approach monitors local spectral invariants that encode admissible operating regions. This paper formalizes the conceptual foundation of HSB and its role as a spectral guardian layer, enabling safe deployment of adaptive and neural controllers in safety-critical software systems.