This appendix presents the full algebraic architecture behind the Matter-Flux Equilibrium Theory (MFET) derivation of the twelve fermion Yukawa couplings, organized as three nested renormalization-group structures with every step shown explicitly. Row 1 selects the substrate through a hyperbolic Möbius map whose form is fixed by the transfer-matrix (PSL(2,ℝ)) structure of one Fibonacci decimation step, with coefficients S = 7φ+2 and P = 17φ+9 following from Vieta's relations and a vanishing offset; its pole at Λ = 0 is identified with the Higgs threshold mode, adjacent to the top quark. Row 2 selects generations through a quintic polynomial map, whose alternating-sign structure permits exactly three stable attractors per substrate separated by regulator-pinned barriers. Row 3 maps each holographic distance Λ to a mass via m = (v/√2)·φ^(−Λ) at the MFET crystallization scale v = 243.5 GeV, yielding charged-lepton masses to ~2% and four parameter-free mass ratios — m_μ/m_e = φ^(φ⁵) = 207.83 (0.5%), m_τ/m_μ = 16.73 (0.5%), m_τ/m_e = 3476.5 (0.02%), m_t/m_b = 40.82 (1.2%) — with no parameters fitted to fermion mass data.