The Binary Recursion Toggle

This paper replaces the QED “axial torsion correction” in the Cohesion UFT finestructure derivation with a geometric mechanism: the Binary Recursion Toggle between
two and only two stable gap configurations of the funneled spring under pressure.
A geometric exclusion proof establishes that n = 3, 4, and 5 gap configurations are
unstable under the Cohesion UFT pressure axiom, leaving only the Hexpolar state
(n = 6, transverse) and the Bipolar state (n = 2, axial) as stable attractors. The
Hexpolar state yields the geometric baseline 1/α6 = 137.029 from the coupling C6 = 3/2
derived previously. The Bipolar state has coupling C2 = 1/2, giving 1/α2 = 137.498.
The CODATA value 137.036 lies strictly between these two states, bounded by:
1
α6
= 137.029 <
1
αCODATA
= 137.036 < θφ = 137.508.
The 0.007 gap between the Hexpolar baseline and CODATA is identified as the geometric
signature of the toggle: the EM vacuum is predominantly Hexpolar with a small Bipolar
participation that reduces the effective coupling from C6 = 3/2 toward C2 = 1/2. The
exact toggle frequency is the one remaining quantity that requires knowledge of the
electron-positron pair production kinematics. The mechanism is purely geometric; the
frequency requires the spectral structure.