Unified Fractal-Stochastic Model (MFSU) — Volume 5 Algebraic Foundation from Tetrahedral Emergent Gravity: Derivation of the Universal Fractal Parameter δF , the Central Dynamical Equation, and the Self-Interaction Coefficient γ

The Unified Fractal-Stochastic Model (MFSU) has postulated since its inception a universal fractal deviation parameter deltaF ≈ 0. 921 governing space-time dimensionality reduction, but has lacked a derivation of this value from first principles. Tetrahedral Emergent Gravity (TEG, Franco Leon 2026, DOI: 10. 5281/zenodo. 19479542) provides exactly this derivation: the holographic codimension partial = 3 − ln 8 ≈ 0. 921 emerges algebraically from a single vacuum geometry axiom—tetrahedral coordination zfund = 4—with zero free parameters. The present work establishes formally that deltaF = partial, constructs the unified TEG-MFSU framework, and derives the central dynamical equation: dψ/dt = −σₑff (−Δ) ^ (ln 8 / 2) ψ + γ |ψ|² ψ + η (x, t), where all coefficients except γ are inherited from TEG without fitting. We further derive γ = σₑff² ≈ 0. 01183 from three independent arguments: (A) the EPRL half-edge closure condition forces the cubic nonlinearity; (B) independent frustration coincidence gives γ = σₑff² for r > rJ; and (C) the global Pohozaev identity gives γgl = Nbits · σₑff², with ratio γgl / γₗoc = Nbits = 3 exact. The framework thereby achieves zero free parameters. Four falsifiable predictions are derived: Hurst exponent H ≈ 0. 780 in the CMB (distinct from the originally postulated H ≈ 0. 541), spectral slope −ln 8 ≈ −2. 079 in the CMB power spectrum, anomalous diffusion exponent t⁰. 962 (NIST), and Tc ∝ γ⁰. 926 (BCS data). The algebraic result H₀ ≈ 70. 2 km/s/Mpc is numerically consistent with the independent CCHP measurement H₀ = 70. 39 ± 1. 22 km/s/Mpc (Freedman et al. 2025), but is not claimed as a prediction since that measurement predates this work.