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 betweentwo 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 areunstable under the Cohesion UFT pressure axiom, leaving only the Hexpolar state(n = 6, transverse) and the Bipolar state (n = 2, axial) as stable attractors. TheHexpolar state yields the geometric baseline 1/α6 = 137.029 from the coupling C6 = 3/2derived 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:1α6= 137.029 <1αCODATA= 137.036 < θφ = 137.508.The 0.007 gap between the Hexpolar baseline and CODATA is identified as the geometricsignature of the toggle: the EM vacuum is predominantly Hexpolar with a small Bipolarparticipation that reduces the effective coupling from C6 = 3/2 toward C2 = 1/2. Theexact toggle frequency is the one remaining quantity that requires knowledge of theelectron-positron pair production kinematics. The mechanism is purely geometric; thefrequency requires the spectral structure.