Article 20: Resolution of PO-1a: Derivation of the Proton Coherence Length ξp

Article 1 introduced the proton vortex coherence length ξ_p = 0.367 fm as a calibrated parameter, leaving its derivation from first principles as open problem PO-1a. This article derives ξ_p without experimental input: ξ_p = C_F · l_P · (1/α_em)^9 = (4/3) · l_P · (1/α_em)^9 = 0.3672 fm (agreement with the Art. 1 calibrated value to 0.052 %). Two independent routes lead to the same result: (i) the non-crossing condition for the three-strand Hopf vortex selects n_p = 9 as the minimal stable harmonic level, with a fractional offset δ = log(4/3)/log(1/α_em) giving exactly the factor 4/3; (ii) the SU(3) colour Casimir C_F = 4/3 in the fundamental representation provides the same prefactor. This establishes that the SU(3) colour structure of QCD is a topological consequence of the three-strand Hopf braid in the PEW framework. All hadronic observables of Article 8 become fully parameter-free. MSC: 81V25 · 81V35 · 83E15 · 11R06 PACS: 12.38.-t · 12.60.-i · 14.20.Dh