Riemann Zero Truncation in Physical Systems: Empirical Evidence for Finite Cosmic Computational Precision

The distribution of non-trivial zeros of the Riemann ζ function exhibits a profound isomorphism with the energy level statistics of quantum chaotic systems (GUE). However, physical observations of these zeros are invariably accompanied by irreducible residual deviations. We propose a physical hypothesis based on the "Cosmic Computational Resolution Limit," suggesting that physical experiments are constrained by the intrinsic precision of the underlying spacetime. Based on the error convergence characteristics of the prime counting function and a P-adic precision layering model, we derive that under the current cosmic evolution scale (maximum prime X ≈ 10⁶⁰) and the precision of the fine-structure constant drift (ε ≈ 10⁻⁴), the upper bound for the physically observable effective Riemann zero height is approximately T ≈ 4200. This theoretical model successfully explains the phenomenon of error breakdown observed at N ≈ 80 in the ion-trap experiment by the University of Science and Technology of China (USTC) under a precision of ε ≈ 10⁻² (theoretical prediction T ≈ 76). Furthermore, we predict that the next effective zero ($N=4201$) will not emerge until approximately 100 million years of cosmic evolution have passed. We also discuss three possible signal characteristics of "redundant zeros" beyond the precision limit, offering a new experimental pathway to verify the finite computational nature of the physical world.