Geometric Action Principle for Unification Yang-Mills, Gravity and matter fermions

A single geometric invariant fixes the relative normalization and structure of gravity, Yang--Mills theory, and fermion kinetic terms. The restricted invariant basis contains known linearized ghost-free quadratic gravitational sectors with propagating torsion. Our results establish a minimal geometric route to unification that does not rely on extra dimensions or symmetry breaking by hand. Unlike previous gauge--gravity constructions, the relative normalizations and ghost freedom emerge from a single Clifford--algebraic invariant.