DOUBLE HELICOIDAL FIELDS AND THE GEOMETRIC ORIGIN OF ELECTRON RAILS (XXXI v6)

In this paper, we formalize the pregeometric mechanism that resolves the scale transition between sub-hadronic throat confinement (E_surface = -0.511 MeV) and atomic orbital chemistry (E_orbital = -13.6 eV). Building upon the Triplet Cancellation Rule established in Part XV, the two Mode-A endpoints of a proton (uud) inherit opposite helicities (h_A1 = +1, h_A2 = -1) and share a common temporal phase clock (Delta phi = 0) transmitted via the common bulk-facing junction, starting at antipodal spatial angles (Delta theta = pi). In the circular-polarization approximation, the linear superposition of these counter-rotating helicoidal fields yields a stationary, non-rotating transverse electromagnetic wave with fixed spatial orientation along the x-hat axis and two antipodal antinodes. These antinodes act as minimum-impedance 'electron rails' in the atomic co-volume, preventing the classical synchrotron decay of Larmor radiation and stabilizing Bohr orbits without phenomenological quantum assumptions. We generalize this construction to variable optical vortex orders l = |m|, showing that the superposition of counter-rotating vortices of order l produces exactly 2l azimuthal lobes, matching the azimuthal multiplicity of real p, d, and f chemical subshells. Finally, we candidly address the 'Polar Challenge' (theta) as an open theoretical debt of the cylindrical single-strand approximation, detailing the required mathematical program for multi-toroidal coupling extensions.