Scaling Limits of an ℓ¹ Causal Lattice: A Structural Framework for Gauge Theory and Gravity

This work develops a constraint-based discrete framework in which aspects of gauge theory, quantum structure, and gravitation arise from a single organizing principle: monotone reduction of local inconsistency under an ℓ¹ coboundary norm. Starting from a minimal discrete configuration, the construction generates a sequence of structures through successive constraints, including a 2-simplex topology, Fourier representation, and a restricted class of transport operators. Within this framework, the admissible operator and symmetry structures are uniquely determined under specified locality, symmetry, and minimality conditions. The resulting structure reproduces key features associated with the Standard Model gauge group SU(3) × SU(2) × U(1), as well as a discrete geometric interpretation of curvature via Regge defects. A hierarchy of effective descriptions emerges through norm transitions (ℓ¹ → ℓ² → ℓ∞), providing a structural relationship between discrete, quantum, and classical regimes. The framework emphasizes constraint propagation rather than parameter fitting. Several quantities arise from structural conditions, while others—such as fermion masses and cosmological parameters—remain explicitly identified as open problems. This work is intended as a constrained construction exploring which aspects of physical theory may follow from general consistency requirements on discrete systems, rather than as a complete or experimentally validated theory.