Arnold's Four Cusp Conjecture for wave-front eversions

Let $\gamma_t$, $t\in[0,1]$, be an eversion of a smooth circular wave front with no dangerous self tangencies: a family of generic oriented wave fronts in $\mathbb{R}^2$ whose endpoints are oppositely oriented smooth circular wave fronts and whose members have no self tangencies at which the orientations on the intersecting strands agree. Arnold's Four Cusp Conjecture. Such an eversion must contain some curves with at least four cusps. The conjecture concerns the cusp structure forced during an eversion of a wave front; the supplied text gives no evidence about whether it has been resolved.