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 framework. The confinement scale is further proved equal to ΛQCD = meφ5Q/4 to 0.3% via the colour Hopf-tower identity ΛUV = vEW/φNc(Nc+1). The universal quark colour level shift δn(C) = 1/2 is proved from the CP2 fibre conformal weight, independent of deff. The quark Koide relation Kup = Kdown = 2/3 is proved exactly at the condensate scale. The complete character table of the binary icosahedral group 2I is given and verified; the four untwisted-sector primaries are identified and the five twisted-sector conformal weights are computed via spectral flow. The weight h2I(s) = 13/90 is proved exactly as the fourth Coxeter exponent of E8 divided by k h(E8) = 90, and the E8 Coxeter assignment of all six SM quarks is proved unique, predicting ms = mμpred with 2.2% agreement. The WEP instanton action S1 = (3/4) · 2−1/3 [(5/4)3/4−1] is derived exactly, giving ηA = exp(−0.108 A) with WEP exact to MICROSCOPE precision for A ≳ 277 baryons. The Hopf fibre U(1) of the colour bundle is identified as the Peccei–Quinn symmetry, giving θQCD = 0 with no beyond-Standard-Model field required. Three CKM mixing angles are derived with no free parameters: |Vus| = √(md/ms) (0.7%), |Vcb| = e−π (3.3%), and |Vub| = √(mu/mt) (4.2%), where |Vcb| is identified exactly as the WZW condensate overlap amplitude. The CP-violating phase is derived at two orders: the leading-order topological spin sum gives δCP(LO) = 17π/40 = 76.5°, and the E8 McKay correction with the exact weight Q/(k h(E8)) = 1/9 gives δCP = 65.0°, within 0.12σ of the PDG value. Sixteen exact or near-exact results are established; a complete tier table is given.