Substrate Quantum Gravity - A Complete Theory of Quantum Gravity

We present a complete framework for quantum gravity based on eight foundational postulates, centered on a complex scalar field — the substrate Φ_P — with a Mexican-hat self-potential and non-minimal coupling to spacetime curvature, plus a discrete-time ontology in which continuous quantum dynamics (Frame 1) is sampled at Planck-scale intervals into discrete observed events (Frame 2). From these postulates, we derive: (i) the Born rule of quantum mechanics, P = |⟨ε|ψ⟩|², from envariance arguments combined with Gleason's theorem applied to the F1→F2 sampling structure; (ii) a propagating massless spin-2 graviton with two physical polarizations, emerging from linearization of the substrate field around its vacuum value, with effective Planck mass M_P²(eff) = M_P²(bare) + 2ξ_P v_P²; (iii) a non-trivial UV fixed point of the renormalization group flow at (g*, λ*, y*, κ_P*, ξ_P*) ≈ (0.72, 0.183, 0.48, 0.067, 0.345) verified through three loops with apparent convergence (R_2 ≈ 0.40); (iv) the Bekenstein-Hawking black hole entropy S_BH = A/(4G) with the universal coefficient 1/4 derived from the heat-kernel computation of the substrate path integral around a Schwarzschild horizon, plus standard logarithmic corrections; (v) CMB observables (n_s, r, f_NL) ≈ (0.967, 0.003, 0.014) atN_e = 60 from substrate-driven inflation, all consistent with Planck 2018; (vi) a stochastic gravitational wave background from a first-order substrate phase transition with peak frequency f ~ 10⁻² Hz and amplitude Ω_GW h² ~ 10⁻¹², within LISA sensitivity. We further establish: holographic correspondence verified at the level of two- and three-point correlation functions plus the conformal Ward identity; a substrate dark matter candidate (the heavy radial mode) with abundance Ω_DM h² ~ 0.1 from gravitational production during reheating; reheating temperature T_RH ≈ 5×10¹² GeV consistent with successful BBN; baryogenesis via leptogenesis matching the observed asymmetry η_B ~ 10⁻¹⁰; and a specific lab-scale prediction of substrate-mediated decoherence γ_dec ∝ m² Δx² in BMV- type mesoscopic interferometry experiments. The framework identifies black holes as substrate-free regions and the Big Bang as a substrate phase transition, replacing curvature singularities with finite, calculable physics. We discuss comparison with other quantum gravity approaches, falsification pathways through LISA, LiteBIRD, BMV, Hyper- Kamiokande, and lattice methods over the coming decade, and open problems including pre-Big-Bang substrate origin and beyond-R² truncations.