Equality of the asymptotic expansions at the focus-node bifurcation

Let $X_-(b)$ and $X_+(b)$ be the two values of the trajectory quantity at the focus-node bifurcation point $b$, obtained from the two distinguished trajectories considered in the paper. The asymptotic-expansion conjecture. The two values $X_-(b)$ and $X_+(b)$ have the same asymptotic expansion. The assertion appears after asymptotic calculations for $X_-(b)$, but no proof or status of this equality is supplied in the given text.