3 problems

Arbitrary-particle-number representability conjecture. The pure excited $v$-representability theorem stated for $N=1$ holds for any $N$, with a sufficient condition that minimizers…

Approximate inverse-potential convergence conjecture. If there exists a potential which exactly produces $\rho$, then the sequence $v_n$ converges to this exact inverse potential i…

Pure-state representability conjecture. The same pure representability result as in dimension $d=1$ holds for $d=2$, whereas the set of potential-representable pure-state densities…