Discrete Spacetime and Space Packets: A First-Principles Derivation of the SV0 Model

This manuscript is the thirteenth and final paper in a series establishing the Signed-Volume Effective-Fluid (SV0) model. In Papers I-XII, we introduced the SV0 model, derived its microphysics, analyzed its perturbations, established its dynamical stability, provided a string-theoretic embedding, constructed a unified cosmological history with an early-universe bounce, resolved the cosmological constant problem, analyzed CMB signatures, and explored its quantum cosmology. In this final work, we provide the ultimate first-principles derivation of the SV0 model by discretizing spacetime geometry. We propose that the universe is fundamentally composed of discrete quanta of volume, or "space packets," and that the continuous volume variables are macroscopic approximations of the number of these packets. The constraint |V_A| + |V_B| = V0 is elevated to a fundamental conservation law of the total number of space quanta, N_A + N_B = N0. We show that the continuous SV0 exchange law emerges as a statistical transition rate between these discrete packets. Most importantly, the Planck-scale regularization factor F(x), previously introduced as a classical cutoff to prevent singularities, is shown to be a natural geometric consequence of the discrete nature of spacetime (the volume cannot be smaller than a single space packet). This establishes the SV0 model as a fully UV-finite, discrete quantum gravity framework. Related Works:Paper I: https://doi.org/10.5281/zenodo.24026844Paper II: https://doi.org/10.5281/zenodo.24032977Paper III: https://doi.org/10.5281/zenodo.24033838Paper IV: https://doi.org/10.5281/zenodo.24034927Paper V: https://doi.org/10.5281/zenodo.24035268Paper VI: https://doi.org/10.5281/zenodo.24035911Paper VII: https://doi.org/10.5281/zenodo.24038624Paper VIII: https://doi.org/10.5281/zenodo.24039486Paper IX: https://doi.org/10.5281/zenodo.24040648Paper X: https://doi.org/10.5281/zenodo.24046082Paper XI: https://doi.org/10.5281/zenodo.24046162Paper XII: https://doi.org/10.5281/zenodo.24046233