<p>Economists and other keen observers have long noted that human capital and institutions bear on growth and well-being, though human capital economics and institutional economics have resisted unification. We demonstrate that these two fields are equally well-described by a single dynamical system: the national economy as a metabolically constrained hierarchy. This structural unity is manifest in the Sovereign Band, a narrow manifold in the plane of institutional capital, <b><i>I</i></b>, and log <i>gdp</i>. Stripped of extraneous constants, the scaling law gdp= e^<i><b>I</b></i> is essential to the condition of economic solvency. By applying the architecture of complex, nested hierarchies—<i>k</i>-tree—to national production, we derive this law from first principles. We identify the economy, <i>in toto</i>, as an invisible <i>k</i>-tree where institutions are its lignified layers of control, balancing the metabolic tax of coordination against the variety-driven surplus of production. We posit that the Industrial Revolution was the nucleation of the first topologically solvent economy, and that the modern spread of growth is the dynamical signature of a phase transition to universal solvency.</p> <div></div>