3 problems

Let $\mathrm{F}_{\alpha}\rbra{P}$ and $\mathrm{F}_{\alpha}\rbra{\rho}$ denote the high-order functionals of a discrete distribution $P$ and a quantum state $\rho$, respectively, an…

Linear-functional extension conjecture. Statements such as $$ should continue to hold for other one-dimensional shape constraints.

Parametric-rate conjecture. The $n^{1/2}$ convergence behavior of linear functionals and the entropy functional should continue to hold for other shape constraints.