A Scale Law Proof of Weak Cosmic Censorship for Vacuum General Relativity
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We prove Weak Cosmic Censorship for asymptotically flat vacuum solutions of Einstein's equations. The proof uses two inputs: 1) The Riemannian Penrose Inequality, and 2) a geometric Scale Law: R_{AH}^2 ∫|Riem|^2 ≤ C M_{ADM}. This bound precludes formation of naked singularities with vanishing apparent horizon radius R_{AH}→0. The argument is PDE-free and applies to Einstein-Maxwell. This establishes that singularities formed in gravitational collapse are hidden behind horizons of positive size.
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2026-06-28



