Information Protection as a Fundamental Principle II: First-Principles Derivation of Spacetime Geometry, Modified Einstein Equations, and Asymptotic Safety from Entanglement

In the first paper of this series, we established the classical information-response dynamics leading to MOND and dark energy. This paper provides the missing rigorous derivation of spacetime geometry and gravitational dynamics from the underlying discrete information network. The network possesses two independent structures: a symmetric adjacency matrix giving the graph Laplacian, whose heat kernel defines the positive-definite spatial metric; and a directed-edge partial order, which independently provides the time function and Lorentzian signature. The effective action for gravity is uniquely determined by the holographic entropy bound, convexity of relative entropy, and the requirement of no hidden mass scales beyond Lambda, yielding the Einstein--Hilbert term plus a unique infrared correction F (Z) = (2/3) (1+Z) ^ (3/2) - 1 for the scalar field kinetic term. Varying this action gives the modified Einstein equations. We then perform an exact renormalization group analysis by coarse-graining the tensor network, deriving the beta functions from first principles (via Dyson Brownian motion of the graph Laplacian) and establishing global asymptotic safety. The absolute convergence of the path integral over tensor network geometries is proven. Finally, we provide a complete first-principles derivation of the dynamic cosmological constant and the information-response function f (H) = 1 - e^ (-2H/H0), yielding the equation of state wDE (H0) approx -0. 910. The present Hubble parameter H0 approx 67. 4 km/s/Mpc is derived from the network topology and the matter content (the latter itself a first-principles output of Papers III and VIII). All results are obtained with zero free parameters.