Relating inclusive e+e- annihilation to electroproduction sum rules in Quantum Chromodynamics

The Broadhurst-Kataev conjecture, that the ``discrepancy'' in the connection with the $\pi^0 \to \gamma\gamma$ anomaly equals the beta function $\beta(\bar{\alpha})$ times a power series in the effective coupling $\bar{\alpha}$, is proven to all orders of perturbative quantum chromodynamics. The use of nested short-distance expansions is justified via Weinberg's power-counting theorem.