This paper writes down the scalar-fermion Lagrangian of the three-plane scaffold and derives from it, without additional postulates, the kink solution, instanton action S0=8/3, Jackiw-Rebbi zero modes, chiral selection rule, generation mass spectrum, and the effective Maxwell equations of electrodynamics at one loop. The central fermionic result is a spectral-flow proof that the trivalent Borromean junction supports exactly one topologically protected left-handed zero mode: the index of the Weyl Dirac operator D_t = igammad + tgphi equals -1 as t increases from 0 to 1, with the protected mode pinned at machine precision (|lambda| < 10^{-15}) throughout and the first massive mode at |lambda| ~ 0.34/delta. This replaces an earlier eigenvalue estimate that was grid-resolution-dependent and is not carried forward. The analytical wall modes psi_z ~ tanh(x)*tanh(y)*sech(z) (and cyclic) are accurate approximations to the exact protected mode; the three modes hybridise at the junction and exactly one survives massless, as the index guarantees. The junction transition matrix element for neutron to proton shows an 8.87:1 preference for left-handed over right-handed emission, establishing a geometric origin for the left-handed weak coupling from the vacuum orientation (+,+,+) without invoking SU(2)_L as a postulate. The electromagnetic sector is derived at one-loop level. The photon is the Berry connection of the protected zero mode. The homogeneous Maxwell equations follow from the Bianchi identity (topological). The inhomogeneous equations follow from the Seeley-DeWitt heat-kernel expansion of the fermion determinant, with the coefficient -1/4 derived explicitly from the Dirac algebra. Charge conservation is topological, enforced by mod-2 flip-parity conservation. The weak sector collective-coordinate description is established: W+/- from junction shear (kappa_theta ~ +996/delta, positive), Z from longitudinal compression. The interaction stiffness kappa_i = 0 exactly for all product-ansatz configurations, proved analytically from the odd-symmetry integral of tanh(x)*sech^2(x). This confirms that the W/Z mass ratio m_W/m_Z = sqrt(7)/3 (0.05% accurate) is purely topological and cannot be obtained from classical junction mechanics. Promoting the collective coordinates to full Yang-Mills gauge fields via the non-Abelian Berry connection of the (u,d) zero-mode doublet is the remaining open derivation. This is a revised version of doi:10.5281/zenodo.19362700, correcting the zero-mode confirmation in Section 5 and updating the weak sector status in Section 8 and the conclusion. All other results are unchanged. Companion papers: Koide relationship and geometric model (doi:10.5281/zenodo.19174656) · LFV prediction (doi:10.5281/zenodo.19202565) · Lepton as 3D apparition (doi:10.5281/zenodo.19203027) · Fine-structure constant from soliton profile (doi:10.5281/zenodo.19211790) · Quark sector, colour, and fractional charge (doi:10.5281/zenodo.19228848) · Mass spectrum and Koide cone (doi:10.5281/zenodo.19267506) · Redistribution prediction for LFV searches (doi:10.5281/zenodo.19301348) · Scalar-fermion Lagrangian, first version (doi:10.5281/zenodo.19361883) · Numerical field data (doi:10.5281/zenodo.19344105).