Before revision:  Interestingly, the bounds show that the structure of the signal does have an impact on the existing bounds of tensor PCA that the unstructured planted signal does not capture .
After revision:  Interestingly, the bounds show that the signal structure impacts the location of the statistical and computational phase transition that the known existing bounds for the tensor-PCA model do not capture. This effect is due to the generic planted signal prior that this latter model addresses .