The zero defect conjecture for aperiodic primitive morphism fixed points

Let ${\mathbf u}$ be an aperiodic fixed point of a primitive morphism whose language is closed under reversal. The palindromic defect $D({\mathbf u})$ is either zero or infinite.

Zero defect conjecture.

$$D({\mathbf u})=0\quad\text{or}\quad D({\mathbf u})=+\infty.$$

This conjecture concerns the possible palindromic defects of aperiodic fixed points of primitive morphisms. It was disproved by counterexamples; the source also records partial positive results for marked morphisms and for fixed points over binary alphabets.