Emergent Spacetime, Matter, and Gauge Symmetry from a Discrete Torsion Lattice

We present a unified, background-independent framework in which spacetime, matter, and gauge interactions emerge from a single discrete lattice endowed with complexified edge connections. The real component of each connection encodes geometric curvature, while the imaginary component governs phase and torsional structure associated with non-contractible loops. Minimization of a global quadratic action simultaneously determines lattice geometry and topological excitations.

Local gauge invariances, including U(1), SU(2), and SU(3), arise naturally from symmetries of the imaginary sector, while stable torsion loops manifest fermionic behavior with intrinsic spin-1/2, chirality, and the Pauli exclusion principle. Sequential lattice updates give rise to an emergent Minkowski metric, light-cone causal structure, and relativistic time dilation.

Discrete topological excitations outside the gauge-aligned sector account for dark matter, and geometric frustration of the lattice vacuum produces an effective cosmological constant. Fundamental constants (c, G, ħ) and the hierarchy of gauge couplings emerge as geometric invariants of the lattice.

This framework provides a logically complete, discrete, and topologically constrained path to unifying the Standard Model, General Relativity, and cosmology, offering specific predictions for high-energy Lorentz violations, discrete renormalization of couplings, and torsion-induced dark-sector dynamics.