Density Entailed Physics - Classification theorem of SM gauge structure in Lie theory.

Classification theorem proving that the complete Standard Model gauge structure — SU(3) × SU(2) × U(1), fundamental representations, three generations, unique Lagrangian — is the sole member of a mathematically defined class of algebraic structures. The classification is exhaustive over the Killing–Cartan catalogue of simple Lie algebras using exact rational arithmetic. Includes the Coordinate-Independent Gauge Structure Theorem (deriving the result from a single axiom), the Classification of Self-Determining Gauge Algebras (a self-contained entry point), and a computational verification script with full results. Formal mathematical basis for the particle physics section of Density Entailed Physics (DOI: 10.5281/zenodo.21755766) the full body of work.