Nam's conjecture on the binding energy of a trapped Bose gas

Let $E(N,\lambda v)$ and $E(N-1,\lambda v)$ denote the ground-state energies of the trapped Bose gas with interaction scaling $\lambda$, and let $T$ and $v$ satisfy appropriate conditions. Assume that $A$ and $C$ are the coefficients specified in Section 5 of Nam's work. Nam's conjecture. As $N\to\infty$ and $\lambda N\to 1$,

$$E(N,\lambda v)-E(N-1,\lambda v)=A+CN^{-1}+o(N^{-1}).$$

This conjecture predicts the leading and next-order terms of the binding energy in the mean-field limit. The paper compares its computed expansion with this prediction and identifies a discrepancy in the coefficient $C$.