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Dynamical Dimensional Reduction on the Sephirotic Graph: 11 Internal Modes to 2 Effective Fields via Fractional Laplacian Decay

Authors: Freeman, Carlos W.;

Dynamical Dimensional Reduction on the Sephirotic Graph: 11 Internal Modes to 2 Effective Fields via Fractional Laplacian Decay

Abstract

We demonstrate that the 11-field coupled PDE system of Multi-Plane Field Syntergic Theory (MPFST), defined on the Sephirotic graph with fractional Laplacian exponent α = 6/5, undergoes spontaneous dimensional reduction from 11 internal modes to 2 effective fields at late times. The mechanism is purely topological: the normalized Laplacian spectrum contains a natural gap Δ = 0.328 between the second and third eigenvalues, the largest gap in the spectrum. Under fractional diffusion (-Δ)^(3/5), modes above this gap acquire topological mass and decay exponentially, while two light modes survive. Mode 0 (λ = 0) is topologically protected, couples universally to all nodes with identical sign, and is identified with gravity. Mode 1 (λ = 0.318) decays 2.7× slower than any heavy mode and partitions the graph into two charge sectors following the bilateral symmetry of the Tree of Life, identified with gauge interaction. The reduction is stable under nonlinear coupling (96% light fraction at g = 1.0). No compactification, no moduli, no landscape — the topology uniquely determines the low-energy content. This resolves the compactification problem without geometric extra dimensions and provides a first-principles derivation of why exactly two long-range interactions (gravity + gauge) exist in nature.

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