Arithmetically Modulated Resonance Dynamics (AMRD): A Synthesis of Stability and Arithmetic

The Arithmetically Modulated Resonance Dynamics (AMRD) framework systematically integrates the spectral stability guarantees of the Resonant Operator Calculus (ROC) with the uniformly bounded, arithmetically defined Leue Modulation Coefficients (LMC). The primary objective is the construction of globally stable discrete dynamical systems where the local evolution parameters are precisely controlled by prime number-based modulation fields. This leads to a novel class of operators, the AMRO M, which possesses a spatially variable symbol, ensuring that local spectral properties can be modulated by arithmetic data while global non-expansivity is inherently maintained by the LMC construction.