Relational Geometric Mechanics IV: The Strong Force — Confinement and the Flux Tube from SU(3) Vector Phase Interference

Paper IV of the Relational Geometric Mechanics series. Derives quark confinement from the SU(3) vector phase component of the RGM wave signature. The vector nature of the color phase introduces a cross-product self-interaction term that vanishes on-axis between color charges and grows off-axis. The variational principle forces the color field into a cylindrical flux tube, producing a linear confinement potential V = σr. Color neutrality as a foam stability condition produces mesons and baryons as the only stable hadron configurations. String breaking follows from the same variational principle. The R³ vector representation used here is a physically correct surrogate for the full SU(3) treatment, which is a formalization target of the series.