The Integer Charge Unit from Spectral Flow: Anomaly Inflow, the Witten Effect, and the Photon Grid of the Vacuum Code

Abstract

The Selection-Stitch Model derives quark charges in thirds from the geometry of a trapped lattice defect. The integer unit that lifts -1/3 to the up-type +2/3 has resisted every mechanism tried: it is not a Cartan charge of the vacuum-matter algebra under the lattice's geometric C and P, and a circuit-ordering geometric phase was excluded by computation. This paper derives the unit from the one place those exclusions left open: the topology of the gauge sector. The framework's electromagnetic channels live on the <100> square faces; the lattice nodes and octahedral voids together form a simple cubic grid, and a compact U(1) on that grid carries monopole defects as a matter of compactness. The chiral defect worldline of the companion paper - directed hopping with point-gap winding W = +1, derived from the verification front - couples to this gauge field, and the pre-registered calculation is a spectral flow: thread one flux quantum through the worldline and count the charge pumped. The answer, computed as a determinant winding and therefore an integer identically, is exactly W: +1 in the physical configuration, 0 in a static crystal, -1 with the frontier inverted, robust across system sizes and every reference inside the point gap. By anomaly matching this boundary flow is the edge of a bulk theta = 2*pi*W, and by the Witten effect flux-bound matter shifts its electric charge by e*theta/2pi = e*W: the charge ladder is q = -1/3 + W, and the up-type +2/3 is derived. Because a determinant winding cannot be fractional, the mechanism cannot touch the thirds: the geometric and topological charges live in different places and add. Two further results follow. The companion matter paper's empirical restriction of the winding to w >= 0 is now derived - negative winding requires an inverted frontier, which the physical configuration forbids - matching the non-observation of charge -4/3; and the framework now requires monopole-type defects of the photon grid, a falsifier-shaped commitment whose microscopic construction is stated as open. Every claim carries a status tag, and the pre-registration rides in the verification archive.