3 problems

Let $F$ be a field of characteristic different from $2$, and let $p$ and $q$ be anisotropic quadratic forms over $F$ of dimension at least $2$. Let $h(q)$ be the height of the spli…

Expected height-two classification. Exactly one of the following holds:

Hoffmann's conjecture. The integer $\mathfrak{i}_{1}(\phi)-1$ is the remainder of $\dim\phi-1$ modulo $2^s$ for some $s<\log_2(\dim\phi)$.