Closed-form muon–electron mass ratio mµ/me = 66 + 87φ to six significant figures from Φ 2 = Φ + 1

The muon–electron mass ratio mµ/me is one of the most precisely measured dimensionlessconstants in physics (PDG: 206.7682838(46)). No first-principles derivation from the StandardModel exists. We show that the single algebraic constraint Φ2 = Φ + 1 (golden root φ) andthe gauge structure at depth k = 4 yield the exact closed-form expression mµ/me = 66 + 87φ,where 66 = d + L5 − 1 and 87 = L4(L6 − F5) − 4 are fixed by the Lucas/Fibonacci sequences(d = 56, L4 = 7, L5 = 11, L6 = 18, F5 = 5). The prediction agrees with CODATA/PDGto six significant figures with zero free parameters. We give the derivation, the structuraldecomposition, and the implications.