Information-Geometry of AdS-Schwarzschild Black Holes: An Exact AdS Correction to the D3 Evaporation Invariant and its Holographic CFT Interpretation

We extend the D3 evaporation invariant to Anti-de Sitter (AdS) black holes. The total D3 displacement is R_total(AdS) = r_s·(1+(r_s/L)²). The two terms have distinct holographic meanings: r_s is the vacuum (T=0) contribution; r_s³/L² is the thermal contribution scaling as T³_CFT — the Stefan-Boltzmann law of a 3D CFT. At the Hawking-Page transition (r_s=L): R_total=2r_s exactly — thermal and vacuum information-geometry costs are equal. The correction factor φ(x)=1+x² is a new holographic observable measuring total-to-vacuum information cost ratio. This is the first D3 result with a complete AdS/CFT interpretation. Verified numerically to four significant figures.