Physics of Discrete Spacetime at the Planck Scale: Dynamic Zero-Point Tunneling and UV Completeness

The Planck scale (10⁻³⁵ m, 10¹⁹ GeV) is the boundary where quantum effects of gravity dominate, but traditional theories face ultraviolet (UV) divergence and spacetime singularity problems. This paper constructs a discrete spacetime model at the Planck scale centered on "dynamic zeros" (the basic quantum units of spacetime/energy), integrating the low-energy quantum gravity effective field theory framework of massless graviton Bose-Einstein Condensate (BEC). We propose a "topological-core + defect compression" strategy for strong-coupling computation: extract the topological core (carrying the main physical information) of the graviton BEC, focus on the topological defects (the source of key effects), and reduce the computational complexity from exponential to polynomial. We prove that the dynamic zero-point tunneling effect eliminates the spacetime singularity at the Planck scale, and the characteristic scale of dynamic zeros (l₀=(1.0±0.1)×10⁻³⁸ m) provides a natural UV cutoff, regularizing the UV divergence in quantum gravity loop diagrams. The model maintains compatibility with Lorentz invariance through discrete covariance of groupoids, and the derived primordial gravitational wave tensor spectrum (tensor-to-scalar ratio r=0.012±0.001) is consistent with current cosmological observations. This work provides a UV-complete discrete spacetime framework and offers testable targets for future high-energy astrophysical experiments.