Lattice Finitism and the Quantitative Derivation of the Lamb Shift: Replacing Virtual Photons with Discrete Arithmetic Friction

The Lamb Shift, the energy discrepancy between 2S1/2 the and 2P1/2 states of hydrogen, is traditionally explained via continuous Quantum Electrodynamics (QED) as the interaction of an electron with a "cloud" of virtual photons. This requires infinite renormalization and the assumption of a continuous Hilbert space. We demonstrate that under the framework of Computational Finitism, the Lamb Shift emerges naturally as a bounded, discrete eigenvalue. By modeling the proton as a localized zero-divisor topological defect and the electron as a stable Möbius knot, we show that the energy shift is the time-averaged difference in Arithmetic Friction (Maintenance Load) incurred by the two states. We present a deterministic cellular automaton simulation yielding a converged energy divergence of Finitist Units. We provide the mathematical dictionary mapping this discrete value to the physical scale, and identify a novel, falsifiable "sawtooth" signature in the energy eigenvalue that distinguishes discrete spacetime from the continuous continuum. We demonstrate that the Lamb Shift is the direct, quantifiable manifestation of the discrete substrate's hardware limits, specifically, the 6-voxel electron knot interacting with the 2-channel TRB architecture through the topological cascade.