Can anyone point me to an easily accessible example of the simplest possible completely monotonic function that is non-realizable by a threshold function? I could only find a 12-dimensional example by E.F. Moore and even that seems quite complicated [1]. Asking because I got into this area while researching to make a video [2] for the summer of math exposition organized by team 3blue1brown.
[1] R. O. Winder, "Single stage threshold logic," 2nd Annual Symposium on Switching Circuit Theory and Logical Design (SWCT 1961), 1961, pp. 321-332, doi: 10.1109/FOCS.1961.29.
[2] https://www.youtube.com/clip/UgkxruXiHNVxGORw8-kILFvtIjh7bU2yYNeV