Torsion Interval Scaling Factors from the Pressure Cascade and Electromagnetic Coupling

The torsion interval scaling factors λ1 ≈ 206.8 and λ2 ≈ 16.8 have been empirical
anchors in the Cohesion UFT mass spectrum since the series began. This paper derives
them from two quantities already established in the series: the zeroth pressure cascade
coefficient C0 = 3/2 and the fine-structure constant α. The first scaling factor is
λ1 = C0/α = (3/2)/α, which predicts λ1 = 205.55, agreeing with the observed ratio
mµ/me = 206.77 to 0.59%. The second scaling factor is λ2 = C0/(4πα) = (3/2)/(4πα),
which predicts λ2 = 16.36, agreeing with the observed mτ /mµ = 16.82 to 2.73%. The
derivation has three steps: the energy of a torsion closure is quantised in units of α (from
E = pr applied to the torsion cycle); the number of available energy units at each closure
level is set by the pressure cascade coefficient C0; and the geometric dimensionality
of successive windings introduces the factor 4π (the solid angle of a sphere) between
the first and second closure levels. The residual 0.59% discrepancy for λ1 is consistent
with sub-harmonic torsion cascade corrections of order α/π, the same mechanism that
produces the anomalous magnetic moment gs − 2. The framework also predicts that
a fourth charged lepton cannot form: the hypothetical λ3 = C0/(16π
2α) ≈ 1.30 falls
below the stability threshold required for a new closure level to persist.