Quasi-Pfister divisibility conjecture for quasilinear forms

Let $n$ be a positive integer, and let $\phi$ be an anisotropic quasilinear quadratic form over $F$ of dimension $2^{n+1}$, with first higher isotropy index $\mathfrak{i}_{1}(\phi)=2^{n-1}$. An $(n-1)$-fold quasi-Pfister form is a tensor product of $n-1$ one-fold quasi-Pfister forms.

Quasi-Pfister divisibility conjecture. The form $\phi$ is divisible by an $(n-1)$-fold quasi-Pfister form.

The conjecture is directly analogous to an open problem for nonsingular quadratic forms and concerns classification in an extremal first-isotropy-index case. Its status is open in the source.