3 problems

Linear diameter conjecture. The cocircuit graph satisfies

Crabbed-path conjecture. There exists a crabbed path from $X$ to $Y$ whose length is no bigger than the length of any path from $X$ to $Y$ in $\operatorname{\mathcal{M}}$.

London–Paris conjecture. There exists a tope $\operatorname{\mathcal{T}}$ in $\operatorname{\mathcal{M}}$ such that $X,Y\in\operatorname{\mathcal{T}}$ and