Quagmires and large Suslin forests

In 1972, Jech asked whether there exists a Suslin $({\omega }_1,{\omega }_2)$-forest in the constructible universe. As reported by Jech, Laver gave a positive answer, but his proof was never published and appears no longer to be available. In 2015, Eskew introduced the combinatorial principle $W_{\kappa }^{\ast }(\lambda )$, a strengthening of Silver’s principle, and used it to construct a coherent Suslin $(\kappa ,\lambda )$-forest. He then asked whether the principle $W_{{\kappa }^{+}}^{\ast }({\kappa }^{++})$ holds in $\mathsf{L}$ for every regular cardinal $\kappa$. We give an affirmative answer to Eskew’s question, thereby also settling Jech’s question.