Strict concavity conjecture for the minimal Riesz energy at exponent minus one

Let $v_s(N)$ be the minimal average standardized Riesz pair-energy of $N$ points on $\mathbb{S}^2$, and define its second discrete derivative by

$$\ddot v_s(N)=v_s(N-1)-2v_s(N)+v_s(N+1),\qquad N>2.$$

Minus-one concavity conjecture. The map $N\mapsto v_{-1}(N)$ is locally strictly concave for all $N>2$, equivalently $\ddot v_{-1}(N)<0$ for all $N>2$. Numerical data suggest this property, but the paper does not provide a proof; it is intended as a necessary criterion for testing putative minimizers.