2 problems

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Nonvanishing of minimizers of the approximate Levy-Lieb functional
Nonvanishing-minimizer conjecture. Any minimizer $\psi$ of $F^{\boldsymbol{\alpha},(0)}(r)$ satisfies
Conjectureopendensity-functional-theory levy-lieb-functional many-body-quantum-mechanicsarXiv posted 2 days ago
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Continuity of the Levy-Lieb and Lieb functionals
Continuity conjecture. If
Conjectureopendensity-functional-theory functional-analysis levy-lieb-functionalarXiv posted 2 days ago