Fukaya's gradient-line and pseudoholomorphic-disc correspondence near a caustic

Let a point of the caustic be fixed, and consider the moduli space of gradient lines and the moduli space of pseudoholomorphic discs associated with the Lagrangian fibration near that point. Fukaya's correspondence conjecture. The moduli space of gradient lines is isotopic to the moduli space of pseudoholomorphic discs in a neighbourhood of a point of the caustic. This conjecture is intended to justify replacing Floer homology and pseudoholomorphic discs by Morse homology and gradient lines near the caustic; the source gives no resolution of the conjecture.