(1.12) An integral affine function on an open subset of $\mathbb{R}^{n}$ is a continuous real-valued function that can locally be written as a degree one polynomial with coefficients in $\mathbb{Z}$. Beware that some authors, including [KS06], allow a constant term in $\mathbb{R}$ in the degree one polynomial; our more restrictive definition is better suited for the purposes of this paper.