Emergent Time from Helical Motion on a Compact Matter Dimension: The Cross-Section Field of the Fibre Angle and the Core of the Charge

In a framework with three-dimensional space, one compact matter dimension and no external time coordinate, a companion paper gave the fine-structure constant the structure 1/α = 2[ln( ¯ λk/a)+c], a logarithm in the cross-section of the matter dimension, with a candidate core of radius √ 8π ℓP that gives 1/α = 137.024 and predicts the neutrino mass quantum k = 4.1155 meV. Five steps of that chain were arguments. We write an explicit action for the field of a twist in the cross-section. The measured scale independence of α fixes its form: it has no gradients along the quota directions, so it is a constraint field and charged particles have no internal excitations. One field for each plane of the quota space, sourced at the core by the holonomy of each cell, induces the Maxwell action with 1/e 2 = s⟨G⟩, independent of the size of the cells, and topology localizes the source. No symmetry fixes the stiffness s; it follows from the saturation principle by which the Planck cell was obtained, applied to phase instead of length. The deficit angle that sets the core is that of general relativity for a line whose tension equals its energy, as the isotropy of the cell requires, and it lies in space, not in the matter dimension. The five steps reduce to principles the companion papers already contain, and no assumption is added. The coherence threshold can no longer float, which sharpens the prediction to k = 4.1155±0.0003 meV. The candidate was selected after it led; only the measurement of k can test it.