We present a self-contained computation showing that the Pati–Salam gaugegroup SU(4)×SU(2)L×SU(2)R and the fermion content of one chiral generationof the Standard Model (including a right-handed neutrino) arise from the geometryof the bundle of pointwise Lorentzian metrics over a four-dimensional spacetimemanifold. The fibre metric belongs to the one-parameter DeWitt family Gλ, andsignature(6,4)—which leads to Pati–Salam via SO(6,4) and its maximal compactsubgroup—obtains for λ1/3. This condition forces λ<−1/3<−1/4, placing the fibre metricin the Pati–Salam regime. The observational constraint from primordial heliumabundance, 0.4<α<0.55, confirms that the entire physically allowed range yieldssignature(6,4). No fields beyond the spacetime metric are introduced. We statewhat this result does and does not establish regarding physical unification.
Lawrence McCurrach (Mon,) studied this question.