Separation of the signed and recursive-line parameters

Construct, if possible, a pair (m,n) for which z_{SL}(m,n)>z_{RL}(m,n), thereby providing an explicit separation between the signed and recursive-line Zarankiewicz numbers.

Background

Although the paper proves equality at (m,n)=(15,6), it does not rule out strict inequality for other parameter pairs. The authors specifically seek an explicit construction analogous to known separations between other augmented Zarankiewicz parameters.

A solution would demonstrate that the signed criterion is genuinely stronger than the recursive-line criterion for at least one doubly simple biquadratic-form instance.

References

Does there exist a pair $(m,n)$ such that

z_{SL}(m,n)>z_{RL}(m,n)?

If so, find an explicit construction, in analogy with Lebedev's separation of $z_A$ and $z_L$ at $m=n=1893$ .

— Is the Signed Zarankiewicz Number the Same as the Recursive-line Zarankiewicz Number?  (2609.20071 - Chen et al., 17 Sep 2026) in Section 5, item 2, “Open Problems”