4 problems

NFM separated-eigenvector conjecture. There exists a scalar $t(k,\bm{\alpha})\in(0.5,1/\sqrt{2})$ such that, for every $j\in[k]$, with probability not converging to $0$ as…

NFM positive-semidefinite subgraph conjecture. There exists a scalar $t(k,\bm{\alpha})\in(0.5,1/\sqrt{2})$ such that, for every $j\in[k]$, $G[V_j']$ satisfies the hypothesis of The…

NFM exact-recovery impossibility conjecture. No algorithm can exactly recover the true clusters in $G$ with probability not converging to $0$ as $n\to\infty$.

Unique nearest-point conjecture. The distance from $P_{0}$ to $\mathcal{V}_{T}^{+}$ is