Stable crossing number conjecture for twist families

Let $\{K_n\}$ be a twist family of knots, and let $\eta$ be its wrapping number. Define the stable crossing number, when the limit exists, by

$$c_s(K_n)=\lim_{n\to\infty}\frac{c(K_n)}{n}.$$

Stable crossing number conjecture. The stable crossing number exists and

$$c_s(K_n)=\eta(\eta-1).$$

The conjecture identifies the asymptotic crossing-number growth with the contribution from the fully twisted region. The preceding diagrammatic estimate gives only the corresponding upper bound.