We extend the ghost wave framework (Godinez 2026a, 2026b) to systems of three identical particles. Applying the indistinguishability principle to the three-particle configuration space C3, we show that the braid group B3 — the fundamental group of the physical configuration space — uniquely determines the color gauge group SU(3)c. The cyclic loop phase theta = 2pi/3 follows from the algebraic identity (s1 s2)^3 = Delta^2 in B3 and the quantization condition on the ghost wave phases derived in Godinez (2026b). The Burau parameter t = exp(2pii/3) generated by this phase produces a representation whose closure is dense in SU(3). We derive all eight Gell-Mann matrices explicitly as Lie algebra generators of B3, identify the Cartan subalgebra with the color quantum numbers I3 and Yc, and obtain a first-principles estimate of the QCD string tension sigma = 0.11 GeV^2 — the only known analytic result with an explicit numerical coefficient derived from topology alone. The effective gluon degeneracy is reduced by a factor of 1/3 relative to the standard result, with observable consequences for the vacuum energy. The framework predicts that gauge groups beyond SU(3) are absent not because the corresponding configuration spaces Cn are topologically forbidden, but because no fundamental multiplets of more than three identical particles exist in nature.