5 problems

Scully's isotropy-index conjecture. One has $k\geq 0$, and

Refined first-isotropy-index conjecture. If $s<2^u+\mathfrak{i}_1$, then

Scully's conjecture. If $q_{F(p)}$ is isotropic, then

Vishik-type isotropy gap conjecture. For every field extension $L/F$, either

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