From UD Theory to Particle Physics: First-Principles Derivation of Gauge Symmetries and Quark Properties

This paper is Part V of the UD theory foundational series, which establishes UD theory as a unified metatheoretical framework for physics. Part I derived general relativity from the scalar projection. Part II derived quantum mechanics from the spinor projection. Part III derived electromagnetism from the vector projection. Part IV derived cosmology from the homogeneous and isotropic limit. This paper derives the fundamental gauge symmetries and quark properties directly from the UD axioms. The four-aspect structure (U_U, U_D, D_D, D_U) has four real components. The total normalization axiom imposes a constraint U_U^2 + U_D^2 + D_D^2 + D_U^2 = 1, which defines a 3-sphere S^3. The tangent space of S^3 is three-dimensional. Complexification yields C^3, whose symmetry group is SU(3). The three dimensions of the tangent space correspond to the three color charges (red, green, blue). Electric charge is defined as the U-D imbalance: ρ_Q = (D_D + D_U) - (U_U + U_D). For the three color degrees of freedom, the dimensionless charge amplitudes q_r, q_g, q_b satisfy q_r^2 + q_g^2 + q_b^2 = 1 from the total normalization axiom. Using the U-D symmetry (q_r = q_g = q_u) and the proton charge +1 (2q_u + q_d = 1), the fractional charges are uniquely determined as q_u = +2/3 and q_d = -1/3, matching the quark model. Confinement follows from the mutual containment principle: a single D_D excitation (quark) lacks the necessary U counterpart and is therefore forbidden. Only color-singlet combinations can exist. The existence of three generations arises from the radial excitation spectrum of the D_D and D_U fields. The potential V(r) = (1/2)m_0^2 r^2 + (λ/4!)r^4 is determined by the UD structural constant πe^π. Numerical solution of the radial Schrödinger equation yields exactly three bound states, corresponding to the three generations of fermions. Quarks are identified as excitations of D_D (D attribute in matter), and leptons as excitations of D_U (U attribute in matter). Spin 1/2 follows from the spinor projection derived in Part II. The Standard Model treats quark properties (fractional charges, three colors, confinement, three generations) as inputs. UD theory derives them from first principles. Series DOI links:Part I (GR): doi: 10.5281/zenodo.19494052Part II (QM): doi: 10.5281/zenodo.19494646Part III (EM): doi: 10.5281/zenodo.19497862Part IV (Cosmology): doi: 10.5281/zenodo.19498260Part V (Particle Physics): this paper