Constructive Derivation of Core Predictions from the Quantum Entanglement Spacetime Theory (QuEST)

The Quantum Entanglement Spacetime Theory (QuEST) postulates a finite-valence hypergraph substrate with irreducible representations of the quantum Lorentz group Uq(so(3, 1)), evolving via local moves and constrained by area–entropy saturation and closure conditions. This work provides a complete, line-by-line, assumption-free derivation of four key predictions from QuEST: the k^4 graviton dispersion with coefficient β = 1/3; a parity-odd component in the Cosmic Microwave Background (CMB) trispectrum; logarithmic timing of black hole gravitational wave echoes; and the logarithmic derivative correlation δ ln ρΛ/δ ln α = 276 between vacuum energy density and the fine-structure constant. All derivations proceed constructively from the four foundational postulates of QuEST, including the inherent prediction of antimatter gravitational asymmetry later confirmed by ALPHA-g 2026.