The twistor-family conjecture for Fukaya–Seidel stability conditions

Let $C$ be a Fukaya–Seidel category, and let ${\sf Stab}_C$ denote its moduli space of stability conditions.

Twistor-family conjecture. The moduli space of stability conditions of a Fukaya–Seidel category can be included in a one-parameter twistor family.

The proposed family is meant to parallel the twistor structures of nonabelian Hodge theory and the Stability Hodge Structure discussed in the source; its general existence is not established.