The Forces: How SU(3)xSU(2)xU(1) Emerges from the Polynomial

In the Standard Model, the gauge group SU(3) x SU(2) x U(1) is an assumption: you write it down and then derive the forces from it. In the GTE framework, the gauge group is a theorem. You start from the 19-bit polynomial and derive which gauge group it implies — without putting any group in by hand. This tutorial explains how the three forces of the Standard Model (electromagnetism, the weak nuclear force, and the strong nuclear force) emerge from the symmetry structure of the GTE polynomial p(L,C,R) = C + R - CR - LCR over GF(7). It covers the derivation of the gauge group, the left-handedness of the weak force, and the V-A structure of weak interactions from first principles.