Robust eigenvectors conjecture for regular simplex tensors

A regular simplex tensor is a tensor associated with a regular simplex, and a frame is the collection of vectors defining that simplex. An eigenvector is called robust when it satisfies the robustness condition for tensor eigenpairs described in Theorem 3.2 of the cited reference.

Robust eigenvectors conjecture. The robust eigenvectors of a regular simplex tensor are precisely the vectors in the frame.

This conjecture concerns whether eigenpairs produced by the tensor power method are robust. The source indicates that the issue was discussed but not comprehensively addressed, and provides no evidence of a resolution.