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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"

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I think the keyword is "rigid". If a point has a transcendental coordinate, then it can be replaced by a variable, as far as polynomial identities go. Then a variable you can, you know, vary. –  Felipe Voloch Dec 16 '10 at 16:03

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