Toward better understanding of energy in economics: Improvements to the Garrett thermodynamic economic model yield a robust system

In a series of papers, Garrett, et al, presents a thermodynamic economic model first laid out in "Are there basic physical constraints on future anthropogenic emissions of carbon dioxide?". This model contains a key conceptual issue that obscures a robust system. This system can link to the Energy Based Cobb-Douglas equation. The key conceptual problem is the belief that $\lambda$, the symbol for growth in Garrett 2011 would disprove the model if it was not constant. However, $\lambda$ cannot be a constant in an economic model, because $\lambda$, with dimension [$\frac{E}{\$ \; GWP}$], represents the aggregate efficiency of all of the more than 359 million firms (and by extension, households) making products globally. To clarify it, I define this aggregate production function distribution as $\Lambda(t) \equiv \sum {\lambda_i(t) \cdot \frac{P_i}{GWP}}$, and with light algebra assign a version of the Energy Based Cobb-Douglas (EBDC) function to $\lambda$. There are various falsified speculations in the body of work that appear to mostly follow from the original issue. The 50 year stable relation of $W$ to $E$ is close, but the trend is not flat. The form and degree to which the "long arm of history" speculation may be true remains to be fully considered, but is falsified in the form presented. The speculation in Garrett 2022 that $\frac{dE}{dt}\rightarrow0$ can cause real GDP to go to zero by inflation is falsified. By generating a dataset going back to -14,000 CE, the speculative $W$ curve appears largely confirmed. The $E$ curve is quite far off prior to 1970 back to 1 CE due to overestimation of pre-industrial energy. By correcting and improving on the foundation issue of Garrett's yeoman effort, improving $E$ and some equation presentation formalism, a robust thermodynamic model of the global economy emerges that is straightforward and practical.