Information-Causality Field and the Unified Field Theory Based on 11-Dimensional T^3 Torus Fractal Geometry -- Paper VII: Topological Thermodynamics and Big Bang Phase Transition: Photon Residuals, Bekenstein-Hawking Limit, and the 1/150 Holographic Entropy Tax in T^3 x Z_900 Vacuum

We present a complete field-theoretical formulation of topological thermodynamics governing the Big Bang phase transition within a discrete T^3 x Z_900 manifold. By replacing the infinite singularity (T → ∞, ρ → ∞) with an upper topological energy density cutoff, the Big Bang is established as a finite, deterministic phase transition of the T^3 vacuum lattice. As the initial lattice de-excites, radiation and matter separate via a topological residual mechanism: photons emerge as open helical shear waves propagating along the 240 coprime phase channels, while mass condenses into closed soliton knots. We derive the maximum attainable cosmic temperature T_max = (ℏc / k_B l_P) √(ρ/κ) ≈ 1.417 × 10^32 K without invoking ad-hoc inflaton potentials. Furthermore, we prove that the 1.6% topological strain margin (δ = 0.016) imposes an exact 1/150 (0.666...%) holographic entropy tax on horizon thermodynamics, yielding a regularized Bekenstein-Hawking horizon entropy S_T^3 = (149/150)(A_H / 4l_P^2) that strictly satisfies the Generalized Second Law. A complete Python numerical pipeline demonstrates that the energy-to-information conversion rate during primordial nucleation obeys Landauer's principle, locking the cosmic photon-to-baryon ratio η_γb ~ 10^9 to pure geometric channel ratios.