3 problems

Let the energy be studied along the line $\gamma=2\pi\beta\kappa$, with real-valued minimizers and $\kappa=\pm 1$. Linear interpolation conjecture. The energy of the real-valued mi…

Statistics-transmutation conjecture. In this ansatz, the energy expectation satisfies

Finer-scale density approximation conjecture. The estimate above can be improved to show that $\varrho^{\mathrm{af}}$ is close to $\varrho^{\mathrm{TF}}_\beta$ on finer length scal…