We prove that the total accumulated D3 information-geometry displacement over complete Hawking evaporation of a Schwarzschild black hole equals exactly the initial Schwarzschild radius: R_total = 2GM₀/c² = r_s(M₀). Five independent constants cancel (M, ℏ, k_B, ln2, π) — only G and c survive. The displacement rate dR/dM = 2G/c² = 1.485 × 10⁻²⁷ m/kg is universal — mass-independent and temperature-independent. Verified numerically to five significant figures across 24 decades of mass. The Schwarzschild radius acquires a new interpretation: it is the exact total information-geometry cost of complete black hole evaporation.