Equality characterizations for the slice Cromwell inequality of homogeneous links

Let $L$ be a homogeneous link. The slice Cromwell equality conjectures. (i) The slice Cromwell inequality

$$\min \deg_v P_L(v,z) \leq 1-\chi_4(L)$$

is an equality if and only if $L$ is positive. (ii) For a homogeneous diagram $D$ of $L$, the inequality

$$\min \deg_v P_L(v,z) \leq -s(D)+w(D)+2s_+(D)+1-2\#_{sp} L$$

is an equality if and only if $D$ is a positive diagram. The slice Cromwell inequality extends Cromwell's inequality from homogeneous links to the smooth four-ball Euler characteristic, while these conjectures seek to characterize positivity through equality in the link-level and diagram-level bounds. The provided source does not indicate whether either conjecture has been resolved.