Quantization—the restriction of observable quantities to discrete values—is widely regarded as a signature of quantum mechanics. In two preceding papers, we have shown that it is not. Wherever a conserved current traverses a multiply connected domain and must return to an equivalent value after projection, integer invariants follow. This holonomic closure condition produces quantum numbers in atoms, flux quanta in superconductors, and orbit numbers in black hole photon rings. Here we show that closed circular DNA satisfies the same three conditions: the phosphodiester backbone is the conserved current, the partner strand is the topological obstruction, and strand closure enforces equivalence after transport. The resulting linking number Lk is computed by the Gauss linking integral—the abelian Chern–Simons functional evaluated on two closed curves in ℝ³. The integer arises from degree theory of the Gauss map, independent of any physical quantization rule. Version history: v1 (February 2026): Initial release. v2 (February 2026): Terminology standardized to covering-space/projection language consistent with companion Papers 1, 2, and 4. "Single-valuedness" replaced throughout with "equivalence after transport/projection." Scale table unified to "covering-space constraint." Conclusion corrected from "geometric" to "topological" constraint. Bibliography updated to current titles and DOIs for Papers 1 and 2. No mathematical content changed.