Kamčev–Morrison conjecture on uncommon minimal rank-2 systems

Let \boldsymbol{[?] be a $(2\times k)$-system, and let $s(\Psi)$ denote the length of its shortest equation, where the length of an equation is the number of nonzero coefficients. A linear pattern is uncommon if it fails the commonness inequality for some 2-colouring. Kamčev–Morrison conjecture. For every even $k\ge 6$, any $(2\times k)$-system $\Psi$ with $s(\Psi)=k-1$ is uncommon. The paper's abstract states that this conjecture is verified for suitably generic pairs of linear equations on an even number of variables; the supplied material does not establish whether the full conjecture is resolved.