I am a mathematical physicist and I am studying certain discrete dynamical systems defined in terms of piecewise linear mappings, which may be expressed in terms of expressions over the max-plus semi-field.

In the study of the points of non-differentiability of these piecewise linear mappings, I was wondering, is there an established proof that (in n-dimensions) every set of points of non-differentiability of a piecewise linear mapping (with rational slopes) may be expressed as the image of a variety over a non-archimedean valuation field under the endowed valuation?

Is there some, possibly constructive proof, with some sort of standard construction?