The relationship between the steady state and the balanced growth path under exogenous technological progress in the Solow growth model is a standard textbook definition in neoclassical economics, requiring no external citation.
The claim states a definitional and foundational property of the neoclassical Solow growth model: when technological progress is exogenous (specifically Harrod-neutral), the steady state (where capital per effective worker is constant) coincides with the balanced growth path (where aggregate variables like output and capital grow at constant rates). This is standard economic theory and common knowledge found in any macroeconomics textbook.