A central theorem of the paper is false: a counterexample satisfies the Cayley criterion yet is not conformally rigid.
Barvinok, A Remark on the Rank of Positive Semidefinite Matrices Subject to Affine Constraints,Discrete Comput
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Conformal Rigidity and Spectral Embeddings of Graphs
A central theorem of the paper is false: a counterexample satisfies the Cayley criterion yet is not conformally rigid.