Independence conjecture for the constructed analytic K3 surface

Let $(X^{an},\Omega)$ be the $K$-analytic K3 surface with volume form constructed from a chosen set ${\cal L}$ of lines. Independence conjecture. The isomorphism class of the pair $(X^{an},\Omega)$ does not depend on the choice of the set ${\cal L}$ of lines. This is motivated by the independence of the period data from ${\cal L}$ and by the Torelli theorem, but the source does not establish the claim.