Stochastic Extensions of the MPFST Coupled PDE System: Noise-Driven Dynamics on the Sephirotic Graph

We extend the deterministic coupled PDE system of Multi-Plane Field Syntergic Theory (MPFST) to include multiplicative and additive stochastic forcing on the 11-node Sephirotic graph. Six computational tests demonstrate noise robustness of the spectral gap, noise-driven meltdown phase transitions, Kramers escape scaling, multiplicative noise stability, stochastic resonance amplification of the gauge mode, and deterministic recovery in the zero-noise limit.