4 problems

Fano hyper-volumes are geometric structures associated with Cayley–Dickson algebras; in the cases discussed, the Fano plane visualises octonion structure and a 15-dimensional Fano…

Positive-signature variant conjecture. The split algebra ${\mathbb A}_{3,1}$ involves variants of ${\mathbb P}_{4}$ with positive signature.

Perspectivity conjecture. For any $N\geq 4$, ${\cal C}_N$ can be regarded as $N-2$ triangles in perspective from a line, such that the points of perspectivity of the…

Grassmannian conjecture. For generic $N$, ${\cal C}_N$ is isomorphic to a combinatorial Grassmannian of type $G_2(N+1)$.