The Full Gauge Structure

The complete internal gauge symmetry is now derived.

SU(3) × SU(2) × U(1)

SU(3). From the gauge freedom of the manifold’s orientation around the break, across three distinct but linked expressions of the manifold (this paper).

SU(2). The weak gauge SU(2), from the freedom in the relationship between the two sectors (AP27). This is distinct from the spacetime spin SU(2) of AP11.

U(1). From the phase freedom of the complex Hilbert space, expressed on the manifold as the electromagnetic connection (AP15).

The symmetry breaking pattern.

SU(3) is exact (the orientation is free). Gluons are massless. Colour is confined.

SU(2) × U(1) is broken to U(1) by Axiom B (the break exists). W⁺, W⁻, Z⁰ are massive. The photon is massless.

The gauge structure of the Standard Model. Derived from {S, B, R, C}.

Step back and look at what you are holding. Four axioms. One governing relation. And the full gauge structure of the Standard Model — the structure that took a century of experiment and theory to discover — falls out as a consequence of the freedom the axioms cannot remove.