Non-Sidorenko conjecture for $(2 \times 5)$-systems

Let $L$ be a $(2\times 5)$-system of linear equations, and let $s(L)$ denote the parameter used in the paper. Assume that $s(L)=4$. Non-Sidorenko conjecture. Every $(2\times 5)$-system with $s(L)=4$ is not Sidorenko. This conjecture arises from the paper's progress toward characterising Sidorenko $(2\times k)$-systems. Apart from the cases established in the paper and the referenced counterexample, the relevant cases remain open.