HopfionSeries Paper V - Colour Confinement, the QCD Scale, and Hadronic Structure from the Hopfion Condensate

We extend the density-feedback Faddeev–Niemi Hopfion framework of Papers I–IV to the strong-interaction sector. The SU(3)C colour structure arises from the CP2 Hopf fibration S1 → S5 → CP2, whose homotopy group π5(CP2) = Z classifies the three colour charges. The semi-Dirac anisotropic dispersion of the condensate gives an effective spatial dimension deffexact = 43/14 (proved here), yielding a UV colour coupling that matches the QCD-running value to 2.4% after the WZW threshold correction Kth = sin(π/5) = √(3−φ)/2. The measured ΛQCD ≈ 208 MeV is bracketed between the exact one-loop formula ΛQCD(1ℓ) ≈ 51 MeV and the two-loop prediction ≈ 544 MeV; the bracketing is a proved structural consequence of the…