Abstract This paper provides a complete, top-down derivation of the existence, structure, and expansion rate of spacetime entirely from the ℜ₁₂ rendering algebra, using zero external physics. We answer three fundamental cosmological questions using a single modular Hamiltonian H_mod = 7: Existence (Q1): Space emerges because the universe's baseline information budget (L = 220) strictly exceeds a single site's processing capacity (N² = 144), mathematically forcing a lattice structure. Structure (Q2): The algebraic real structure uniquely fixes the KO-dimension, selecting a (3+1) Lorentzian signature. Expansion (Q3): Cosmic expansion is the irreversible thermodynamic arrow of rendering. We derive the exact Hubble constant (H₀ = 66.18 km s⁻¹ Mpc⁻¹) as an Arrhenius rate of modular vacuum escape, governed by the Landauer information-erasure cost. No general relativity.No Friedmann equation.Zero free parameters. Everything is derived strictly from the ℜ₁₂ algebra.