  Within ``orbital-free'' density functional theory, it is essential to develop
general kinetic energy density (KED), denoted as $t(\mathbf{r})$. This is
usually done by empirical corrections and enhancements, gradient expansions,
machine learning, or axiomatic approaches to find forms that satisfy physical
necessities. In all cases, it is crucial to determine the largest spatial
density derivative order, $m$ in, $t(\mathbf{r})$. There have been many efforts
to do so, but none have proven general or conclusive and there is no clear
guide on how to set $m$. In this work, we found that, by imposing KED finitude,
$m=D+1$ for systems of dimension $D$. This is consistent with observations and
provides a needed guide for systematically developing more accurate KEDs.
