Clunie and Sheil-Small's coefficient conjecture for normalized harmonic mappings

Let $f=h+\overline{g}\in\mathcal{S}^0_H$ have the power-series representation

$$h(z)=z+\sum_{n=2}^{\infty}a_nz^n,\qquad g(z)=\sum_{n=1}^{\infty}b_nz^n.$$

Clunie–Sheil-Small coefficient conjecture. For every $n\geq2$,

$$|a_n|\leq\frac{(n+1)(2n+1)}{6},\qquad |b_n|\leq\frac{(n-1)(2n-1)}{6},\qquad \bigl||a_n|-|b_n|\bigr|\leq n.$$

This is a central coefficient problem for sense-preserving univalent harmonic mappings, analogous to the Bieberbach conjecture for analytic univalent functions. The source identifies it as an open question.