Ore-type toughness conjecture for hamiltonicity

Let $G$ be a $t$-tough graph on $n\ge 3$ vertices. Define

$$\sigma_2(G)=\min\{d_G(u)+d_G(v):u,v\in V(G),\ u\text{ and }v\text{ are nonadjacent}\}$$

for noncomplete $G$, and set $\sigma_2(G)=\infty$ when $G$ is complete. A graph is hamiltonian if it contains a hamiltonian cycle.

Ore-type toughness conjecture. If

$$\sigma_2(G)>\frac{2n}{t+1}-2,$$

then $G$ is hamiltonian.

The statement strengthens the paper's proved Ore-type condition by removing the additive $t$ term. It is presented as a stronger statement that might be true and remains open.