The Velado Bound: A Geometric Lower Bound on Adversarial Detectability via Fisher-Rao Information Geometry

We prove a fundamental lower bound on adversarial perturbations in conservation-constrained probability systems. For states x, x' on the probability simplex S_n lying in different entropy bands, the product of Fisher-Rao geodesic distance D and semantic impact I satisfies D·I ≥ κ, where κ = (ΔH)²/M emerges from simplex geometry. The bound is derived via Cauchy-Schwarz inequality on the Fisher-Rao manifold and establishes a geometrically forbidden region where high-impact, low-detectability attacks cannot exist. We call this the Adversarial Uncertainty Principle. Empirical validation on H100 GPU confirms the forbidden quadrant {D<0.5, I>0.5} remains empty across 10⁵ trials. Priority: U.S. Provisional Application No. 63/958,306, filed January 12, 2026.