The Primordial Energy Waves (PEW) framework addresses open problemPO-Leptons: derive the muon and tau masses from PEW geometry. This article establishes two results and documents a third. (i) HARMONIC LEVELS B: The three charged lepton masses correspond to harmonic levels nₑ = 10. 473, nₘu = 9. 389, nₜau = 8. 815 in the PEW table lambdaₙ = lP * (1/alphaₑm) ⁿ. The span nₑ - nₜau = 1. 657 ≈ 1 + 1/phi = 1. 618 (agreement 2. 4%). (ii) KOIDE RELATION AS PEW SIMPLEX A: The empirical Koide relation K = (mₑ + mₘu + mₜau) / (sqrt (mₑ) +sqrt (mₘu) +sqrt (mₜau) ) ² = 2/3 (9. 2 ppm from CODATA) is identified as the leptonic simplex condition: the vectors xᵢ = sqrt (mᵢ) /sum (sqrt (mⱼ) ) form a regularsimplex with sum xᵢ = 1 and sum xᵢ² = 2/3. The ratio 2/3 = CF/2 connects to the SU (3) colour Casimir CF = 4/3 (Article 20). This is the exact leptonic analogue of the proton quark charge simplex established in Article 22. (iii) CANONICAL PARAMETRISATION A: In the Brannen parametrisation sqrt (mᵢ) = A (1 + sqrt (2) *cos (theta₀ + 2*pi* (i-1) /3) ), the correct amplitude is rho = 1, giving theta₀ = 2. 3166 rad (132. 73°), which exactly reproduces all three lepton masses. The phase theta₀ = 2. 3166 rad has no known PEW expression to better than 10%; PO-Koide-phase remains open D.
Michel ALdon (Sat,) studied this question.