Stochastic Extensions of Fractional PDE Dynamics on the Sephirotic Graph: Noise-Robust Dimensional Reduction and Meltdown Transitions

VERSION 2 — Corrected to use canonical Paper 9 spectrum values. λ₁ updated from 0.318 to 0.291, spectral gap from 0.328 to 0.458. Original abstract: We extend the deterministic 11-mode Sephirotic PDE of MPFST to include stochastic forcing, modeling environmental noise, measurement uncertainty, and quantum fluctuations. Five noise types are tested: white, colored (1/f), multiplicative, shot, and Lévy. All preserve the 2-light-mode dimensional reduction established in Paper 14. Kramers escape rates predict meltdown transitions between basins of attraction. The fluctuation-dissipation relation generalizes to fractional order α = 6/5. Stochastic resonance amplifies weak coherent signals near the spectral gap frequency.