Eventual linearity conjecture for crossing numbers in twist families

Let $\{K_n\}$ be a twist family of knots with wrapping number $\eta$.

Eventual linearity conjecture. For sufficiently large $n$,

$$c(K_{n+1})=c(K_n)+\eta(\eta-1).$$

This is a more precise version of the stable crossing number conjecture: it predicts that the crossing number eventually increases by the exact contribution of one additional full twist.