Conway's common-refinement conjecture for generalized power series

Let $K((\mathbb{R}^{\leq 0}))$ be the ring of generalized power series with exponents in $\mathbb{R}^{\leq 0}$. For a factorisation $a=b_1\cdot\ldots\cdot b_n$, a refinement is a factorisation obtained by further factoring each $b_i$, up to reordering and multiplication of factors by constants in $K^*$. Conway's conjecture. For every non-zero series $a\in K((\mathbb{R}^{\leq 0}))$, any two factorisations of $a$ admit common refinements. This predicts a strong compatibility between the generally non-unique factorisations of generalized power series; examples such as monomials and polynomials support it, but the assertion remains open in the supplied source.