Jeffrey Wang in Section 4.2 writes "Since a code is the solution to a number of polynomial equalities between the shortest edges, the coordinates of each rigid point in the code are algebraic and lie in a number field."[1]

Is his assertion mathematically provable? Where might this be found? (I am new to this field)

[1] arXiv: 0805.0776v2 "Finding and Investigating Exact Spherical Codes"