Emergence of Gauge Symmetries and Fermions in the SV0 Model: A Discrete Spacetime Approach to the Standard Model

This manuscript is the fifteenth and final paper in a series establishing the Signed-Volume Effective-Fluid (SV0) model. In Papers I-XIV, 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, explored its quantum cosmology, provided a discrete spacetime derivation, and explained baryogenesis. In this final work, we address the origin of the Standard Model of particle physics within the discrete spacetime framework of the SV0 model. We propose that the fundamental "space packets" possess internal topological degrees of freedom. We demonstrate that the two signed-volume sectors (V_A > 0 and V_B < 0) naturally give rise to the chiral structure of fermions, with the exchange law governing the mixing between left- and right-handed states. Furthermore, we show that the connectivity of the discrete space packets forms a lattice whose automorphism group spontaneously breaks into the Standard Model gauge group SU(3) x SU(2) x U(1). The SV0 exchange parameter γ acts as the unified coupling constant at the Planck scale, and the Higgs mechanism emerges from the background volume fraction x = 1/2. This work completes the SV0 journey, establishing it as a comprehensive Theory of Everything that unifies dark energy, early-universe cosmology, quantum gravity, and particle physics. 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.24046233Paper XIII: https://doi.org/10.5281/zenodo.24046352Paper XIV: https://doi.org/10.5281/zenodo.24046520