CPU 2.0: A Verifiable Lean 4 Simulation Framework for Quantum Spacetime Quantization and Gravitational Clock Drift

This paper introduces CPU 2.0, a novel digital physics simulation framework formally verified using the Lean 4 interactive theorem prover. By modeling spacetime as a discrete computational lattice at the Planck scale (lp = 1.616255 × 10^-35 m), we derive falsifiable consequences from the hypothesis that the universe is a computational system. We formalize 10 core theorems covering noise propagation, information density, and gravity as computational overhead. A key prediction is a quantized deviation from General Relativity: for a typical neutron star (M = 2.8 × 10^30 kg, r = 12,000 m), temporal discretization produces a deterministic clock drift of 1.11 × 10^-16 s/s, or 3.5 ns/year. This provides a direct, empirically testable metric for Pulsar Timing Arrays and next-generation satellite observations.