3 problems

Stabilization conjecture. In the Gaussian setting of Theorem 1, the expected number of critical points of $d_v$ on $X$ does not decrease when $n_p$ is replaced by $n_p-1$.

Generic uniqueness conjecture. Every $\mathcal{T}\in\mathbb{R}^{n_1\times\cdots\times n_d}$ has a unique rank-one approximation, unless $\mathcal{T}$ lies on a subvariety; moreover…

Let $\underline{\bf X}$ be a tensor in orbit $D_3$, and let $\underline{\bf Y}$ be a best rank-$1$ approximation of $\underline{\bf X}$. Orbit $D_3$ stability conjecture. Almost al…