Sparse curve singularity delta-invariant conjecture

Let $B_1,\ldots,B_k\subset\mathbb Z^1_{\geqslant 0}$ be support sets, let $d_i:=\min B_i>0$, and let

$$j_r:=\operatorname{GCD}\,\bigcup_i(B_i\cap[d_i,d_i+r]).$$

Assume that $j_\infty=1$, equivalently that the associated map germ is injective. Sparse curve singularity delta-invariant conjecture. For arbitrary $k$, the $\delta$-invariant of the sparse curve singularity in $\mathbb C^k$, whose components are supported at $B_1,\ldots,B_k$, equals

$$\text{a function of }d_1,\ldots,d_k+\sum\limits_{r=0}^{\infty}\dfrac{j_r-1}{2}.$$

This extends the proved formula for $k=2$, where the first term is $\frac{(d_1-1)(d_2-1)}2$. The conjecture seeks a support-set formula for basic invariants of sparse curve singularities in arbitrary target dimension.