Equality of the signed and recursive-line Zarankiewicz numbers

Determine whether the signed Zarankiewicz number satisfies z_{SL}(m,n)=z_{RL}(m,n) for every pair of positive integers m,n.

Background

The paper establishes z_{RL}(15,6)=60, which, together with the previously known value z_{SL}(15,6)=60, removes the only known candidate for strict inequality between the signed and recursive-line Zarankiewicz numbers. The authors therefore leave unresolved whether the two parameters are equal for all dimensions.

This problem concerns the general relationship in the chain z_2(m,n)\ge z_{SL}(m,n)\ge z_{RL}(m,n), and asks whether the second inequality is always an equality.

References

Is it true that

z_{SL}(m,n)=z_{RL}(m,n)

for all $m,n$? The case $m=15$, $n=6$ no longer provides a counterexample, but no general proof is known.

— 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 1, “Open Problems”

The general problem remains: is z_{SL}(m,n)=z_{RL}(m,n) for all m,n, or is there a pair (m,n) with z_{SL}(m,n)>z_{RL}(m,n)?

— Exact Second-Order Zarankiewicz Numbers for Complete-Graph Incidence Families  (2609.25974 - Chen et al., 22 Sep 2026) in Section 5, Open problems, item 6