Gauge Structure of the Standard Model from Torsion Phase Geometry

The Standard Model of particle physics is built on the gauge group U(1)×SU(2)×SU(3),imposed as a symmetry principle from outside the theory. This paper derives these threegauge groups from the torsion phase geometry of the Cohesion Unified Field Theoryrecursion field. The derivation rests on a single observation: the absolute structuraltime phase at any point in the recursion medium is not an observable — only differencesin structural time phase are physically meaningful. This local phase freedom is notimposed; it is a consequence of the nature of structural time. Demanding that thephysics be invariant under local structural time rephasing generates each gauge groupfrom the corresponding recursion mode: U(1) from the single phase variable of the n = 6hexapolar recursion, generating electromagnetism; SU(2) from the two-component phaserotations of the n = 2 bipolar recursion, generating the weak interaction; and SU(3)from the three slip-phase rotations of composite baryon recursion, generating the stronginteraction. The gauge connection fields — the photon, W±/Z0 bosons, and gluons —are the recursion phase connection fields required to maintain local phase invariance.The electroweak unification group SU(2) × U(1) arises from the phase degeneracy ofthe n = 2 and n = 6 modes at high density. This is the first derivation of the StandardModel gauge structure from the torsion phase geometry of the Cohesion UFT recursionfield.