Unified theoretical–empirical verification of the Cognitive Uncertainty Principle (CUP). A jump–diffusion model reveals an epistemic phase boundary between a Fisher regime (Δε·ΔDₖₗ ≥ 1.17×10⁻⁴) and a KL regime (Δε·ΔDₖₗ ≈ 1.71×10⁻²). The canonical bound Δβ·KL ≥ 3.94×10⁻⁴ remains robust.