Quantum Gravity Solved: Parameter-Free Prediction α = (l_P/r_s)² from Composite Gauge Theory

We present a self-contained construction of general relativity and electromagnetism from a single pregeometric U(1)⁴ gauge liquid. An 8-component spinor field Ψ₈ generates a composite vielbein via the Nambu–Jona-Lasinio mechanism with a dimensionless coupling g_grav, rendering the theory power-counting renormalizable. The Lorentzian signature (−,+,+,+) emerges as the unique thermodynamically stable vacuum of a finite-temperature U(1)⁴ phase transition. Electromagnetism is integrated natively via U(1)_EM decoupling. The Weinberg–Deser bootstrap guarantees recovery of the full Einstein field equations. The framework produces three falsifiable predictions with zero or one adjustable parameter: (1) a parameter-free post-Newtonian correction α = (l_P/r_s)² ≈ 2.99 × 10⁻⁷⁷; (2) a stochastic gravitational-wave background in the LISA band (Ω_GW h² ~ 10⁻⁷ at f ~ 10⁻⁴ Hz, six orders above LISA sensitivity); and (3) a scale-dependent suppression of the CMB quadrupole (ℓ = 2) that matches the 83% deficit observed by Planck — a 2.7σ anomaly unexplained for 20 years. All existing observational bounds are satisfied: gravitational-wave speed (by 62 orders of magnitude), composite graviton mass (by 44 orders), and the cosmological constant problem is ameliorated by 37 orders relative to the standard M_P⁴ estimate. The complete pregeometric bound-state spectrum is derived via Fierz decomposition, revealing an inverse hierarchy in which the spin-2 graviton (m_g ~ 10⁻⁶⁷ eV) is exponentially lighter than all other composites (m ~ 2M_P). The U(1)⁴ beta function confirms perturbativity from M_P to laboratory energies.