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 delta_F ≈ 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 z_fund = 4—with zero free parameters. The present work establishes formally that delta_F = partial, constructs the unified TEG-MFSU framework, and derives the central dynamical equation: dψ/dt = −σ_eff (−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 = σ_eff² ≈ 0.01183 from three independent arguments: (A) the EPRL half-edge closure condition forces the cubic nonlinearity; (B) independent frustration coincidence gives γ = σ_eff² for r > r_J; and (C) the global Pohozaev identity gives γ_gl = N_bits · σ_eff², with ratio γ_gl / γ_loc = N_bits = 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 t^0.962 (NIST), and T_c ∝ γ^0.926 (BCS data). The algebraic result H_0 ≈ 70.2 km/s/Mpc is numerically consistent with the independent CCHP measurement H_0 = 70.39 ± 1.22 km/s/Mpc (Freedman et al. 2025), but is not claimed as a prediction since that measurement predates this work.