A Relational Simplicial Framework for Geometry and Standard-Model Gauge Fields

We formulate a common discrete configuration space in which edge lengths encode piecewise-flat geometry, a causal orientation defines a partial order, and compact gauge holonomies on the same oriented edges represent the local gauge group of the Standard Model. A single formal configuration sum combines a four-dimensional Regge gravitational action, Wilson-type gauge actions, a Higgs sector, and a chiral matter sector. We derive the local gauge-transformation laws and show that face-trace actions are gauge invariant. We state a conditional stability result for a finite Euclidean edge regulator and explain why it does not establish stability of the full Lorentzian gravitational path integral. On a regular-lattice regulator, the standard low-momentum lattice dispersion is recovered as a calculation within the regulator, not as a prediction of the irregular dynamical network. The Newtonian limit is recovered conditionally if the geometry sum has a continuum phase governed by the Einstein–Hilbert action. This construction is a synthesis/ansatz, not a demonstrated Theory of Everything: the measure over complexes, the chiral lattice fermion operator, renormalized continuum limit, and a derivation of the Standard Model parameters remain unresolved. The common carrier of interactions should not be confused with unification of their couplings or symmetries. Acknowledgements: The author expresses gratitude to family, peers, and independent researchers for technical feedback on the mathematical infrastructure. Computational synthesis, linguistic polishing, and manuscript structural formatting assistance were supported by large language model AI assistants (Gemini and ChatGPT).