Existence, Uniqueness, and Stability of the Coupled 11-Field Fractional PDE System in Multi-Plane Field Syntergic Theory

We establish the rigorous mathematical foundations for the coupled 11-field fractional partial differential equation system that constitutes the dynamical core of Multi-Plane Field Syntergic Theory (MPFST). Using the Sephirotic coupling topology — an 11-node, 24-edge graph whose normalized Laplacian has an exact eigenvalue at α = 6/5 — we prove: (1) Local existence and uniqueness via Banach fixed-point theorem in fractional Sobolev spaces; (2) Global energy dissipation under a coercivity condition on the coupling matrix; (3) Continuous dependence on the fractional index α, with Lipschitz stability estimates; (4) A spectral resonance theorem showing that α = 6/5 uniquely maximizes coherent energy transfer…