2 problems

Smallest-example conjecture. For $n=7$, the constructed example is the unique smallest example in the Grassmann graph of planes of ${\rm PG}(7,q)$.

Classification conjecture. If $\mathcal{I}$ is a negative intriguing set of $\mathcal{G}\setminus P^\perp$, then either there are points $Z_1,\ldots,Z_n$ of $P^\perp$ such that