The trace-forest content formula conjecture for skew tableaux of hook shape

Let $\lambda$ and $\mu$ be partitions with $\lambda\vdash n$, and suppose that $\mu$ is a hook. Write $f^{\lambda/\mu}$ for the number of standard Young tableaux of skew shape $\lambda/\mu$, and let the content of a cell $w$ be $c(w)=\operatorname{column}(w)-\operatorname{row}(w)$. Trace-forest content formula conjecture. The scheme based on the trace forest of jeu de taquin always gives a formula for $f^{\lambda/\mu}$ in terms of the contents of the cells of $\lambda$. The conjecture would extend the paper's bijective character-evaluation method from the displayed examples to every hook $\mu$; although the corresponding character evaluations are known algebraically, the source notes that no combinatorial proof is known.