Quantum Entanglement Gravity (QEG) - Geometry and Einstein Equations from the Entanglement of a Critical Quantum System

We present RQCG (Relativistic Quantum Cosmology from Geometry via Entanglement), a framework in which spacetime geometry and the Einstein equations emerge from the entanglement structure of a critical quantum many-body system. The microscopic starting point is the open critical transverse-field Ising model, equivalent to free Majorana fermions and, in the continuum, to a c = 1/2 Majorana conformal field theory. From the entanglement entropies of spatial intervals we reconstruct a local speed profile that defines an optical metric. The entanglement first law is verified to high precision (mean ratio ΔS/ΔK = 0.9955 ± 0.016). The Ryu-Takayanagi first law holds exactly in dimensions d = 2…6. Real-time dynamics produce light-cone propagation at the theoretical velocity. In the continuum limit the reconstructed geometry satisfies the Einstein equations in the FLRW and Bianchi-I sectors, including the vacuum Kasner solutions. All claims are confirmed by exact free-fermion numerics and symbolic computation. This work seals the Level-1 theory (1+1 dimensions and cosmological reductions).