Quantum Field Theory as the Long-Wavelength Limit of Planck-Scale Discrete Spacetime: UV Completion, Vacuum Energy Drainage, and Cosmological Running of Coupling Constants

Quantum field theory carries two unresolved structural problems: ultraviolet divergences requiring renormalisation, and a vacuum energy density 10¹²⁰ times larger than observed. We argue both problems have a common origin — continuous spacetime — and both are resolved when spacetime is treated as a discrete Planck-cell network. The Planck length provides a physical UV cutoff, rendering QFT automatically finite. The vacuum energy decreases continuously over cosmic time as the Planck length grows (ρᵥac ∝ c⁶), reframing the cosmological constant problem as cosmic evolution. QFT is entirely preserved as the correct effective field theory at all sub-Planckian energies. A new testable prediction: coupling constants should exhibit a small cosmological time evolution driven by the evolving Planck length, testable with the ELT/ANDES spectrograph at z < 1. This is Paper 5 in the Pixel Theory series. Companion papers: Paper 1: https: //doi. org/10. 5281/zenodo. 20491684 Paper 2: https: //doi. org/10. 5281/zenodo. 20529501 Paper 3: https: //doi. org/10. 5281/zenodo. 20530178 Paper 4: https: //doi. org/10. 5281/zenodo. 20525925 Paper 6: https: //doi. org/10. 5281/zenodo. 20585009 Paper 7: https: //doi. org/10. 5281/zenodo. 20540035