Cognitive Uncertainty Principle: Dual Empirical–Theoretical Verification via Jump–Diffusion Dynamics

Version 2.0 unifies theoretical and empirical verification of the Cognitive Uncertainty Principle (CUP).A generative jump–diffusion model analytically links perceptual resolution (ε) and information divergence (Dₖₗ) through Fisher-information geometry, establishing the boundΔε · ΔDₖₗ ≥ C (1.17×10⁻⁴).Large-scale simulations confirm consistent constants C_β = 3.94×10⁻⁴ and C_ε = 1.71×10⁻², demonstrating that observer entropy dynamics obey a reproducible information–theoretic limit.The work formalizes CUP as a quantitative law connecting Fisher information, observer entropy, and generative cognitive processes.