Geometric Cost of Information Erasure: A Schwarzschild-Radius Formulation of the Landauer-Einstein-Schwarzschild Identity

We derive an explicit Schwarzschild-radius form for the geometric effect of erasing one bit of information at temperature T. Combining Landauer's principle, Einstein's mass-energy equivalence, and the perturbative Schwarzschild radius shift, we obtain: Δr_s = 2G·k_B·T·ln(2)/c⁴. The central result is an exact Planck coincidence: Δr_s(T_P) = 2·ln(2)·l_P, where all four fundamental constants cancel algebraically.