Photon-Sea v1.2 Stability and Consistency Analysis of the MyominAung Photon-Sea Lagrangian

This supplementary document provides a rigorous mathematical stability and consistency analysis of the Lagrangian formulation within the MyominAung Photon-Sea Theory of Everything (MATE). It addresses the fundamental requirements of theoretical viability, including the boundedness of the Hamiltonian, the absence of ghost degrees of freedom, and the well-posedness of the non-linear equations of motion. A key finding is the dynamic stability of the zero-frequency ground state, where inverse-frequency divergences act as a physical saturation mechanism rather than a mathematical pathology. This stability provides a formal justification for identifying low-frequency configurations with the observed properties of dark matter.