Stability of eigenvectors of equiangular tight frame decomposable tensors

Let $\mathcal{T}$ be an equiangular tight frame decomposable tensor, meaning a symmetric tensor admitting a decomposition into powers of vectors from an equiangular tight frame. The stability conjecture. The eigenvectors of an equiangular tight frame decomposable tensor are stable under perturbation and can be approximately recovered using the tensor power method. This is proposed by analogy with the known stability of eigenvectors of orthogonally decomposable tensors; the source says it is strongly supported by numerical experiments but does not establish it.