Theory of Dynamic Resonant Emergence (TDRE): A Complete and Self-Contained Formulation from Foundational Postulates to the Rigorous Derivation of the 8 x 12 Stability Lattice

We present a complete and self-contained formulation of the Theory of Dy- namic Resonant Emergence (TDRE), incorporating all foundational developments from the original continuous Lagrangian framework through the discrete hexago- nal plenum formulation. Starting from nine operational postulates, we derive: a covariant Lagrangian for a CP1 doublet field coupled to a gauge potential and stabilised by a Skyrme-type term; the emergence of Coulomb/Maxwell elec- trodynamics and gravity as low-energy limits of a single unified gauge sector; a discrete hexagonal plenum whose point group D6 ×Z2 arises from lattice geometry rather than postulate; complete dispersion relations for all nine normal modes of the plenum; and, as the central mathematical result, the 8 ×12 stability lattice of admissible vortex modes, whose bounds nmax = 8 and mmax = 12 are structural consequences of the adopted assumptions, derived independently from two arguments each.