The splice-diagram decomposition conjecture for Milnor fibers

Let $\Delta$ be a splice diagram satisfying the semigroup conditions, and write \Sigma=\Sigma_1~\raise5pt\text{\underline{K_1\quad K_2}}~\Sigma_2 for the decomposition obtained by cutting $\Delta$ at an edge. Let $F_1$ and $F_2$ be the Milnor fibers of the corresponding complete intersection singularity links, let $G_i$ be the associated Milnor-fiber surfaces, and set

$$F_1^o:=F_1-(G_1\times (D^2)^o),\qquad F_2^o:=F_2-((D^2)^o\times G_2).$$

Splice-diagram decomposition conjecture. The Milnor fiber $F$ is homeomorphic to the result $\overline F$ of pasting

$$\overline F:=F_1^o\cup_{G_1\times S^1}(G_1\times G_2)\cup_{S^1\times G_2}F_2^o,$$

where $G_1\times S^1$ is identified with $G_1\times\partial G_2$ and $S^1\times G_2$ with $\partial G_1\times G_2$.

This was proposed as an iterative description of Milnor fibers in terms of simpler complete intersection surface singularities. The source presents it as conjectural and gives no general resolution statement.