### Abstract or Additional Information

A major goal of quantum computing research is to drain all quanta \(q\) of thermal energy from a solid at a positive temperature \(T_{0}>0,\) leaving the object in its ground state. In 2010 the first complete success was reported when a quantum drum was cooled to its ground state at \(T_{0}=20{\rm mK.}\) However, current theory, which is based on the Bose-Einstein equation, predicts that temperature \(T \to 0\) as \(q \to 0\).

We prove that this discrepancy between experiment and theory is due to previously unobserved errors in low temperature predictions of the Bose-Einstein equation. We correct this error and derive a new formula for temperature which proves that \(T \to T_{0}>0\) as \(q \to 0\). For experimental data our temperature formula predicts that \(T_{0}= 9.8{\rm mK}\), in close agreement with the \(20{\rm mK}\) experimental result.