Hyperplane classification conjecture for Veronese spaces over polar spaces

Let ${\goth M}:=\VerSpace(k,\PolarSpace(\varpi))$, and let ${\mathscr H}$ be a hyperplane of \VerSpace(k,\text{\boldmath\goth P}) determined by a polarity $\varkappa$. The intersection

$${\mathscr H}\cap{\mathfrak y}_k(Q_0(\varpi))$$

is a hyperplane in ${\goth M}$. Hyperplane classification conjecture. The hyperplanes of ${\goth M}$ are precisely those of the form

$${\mathscr H}\cap{\mathfrak y}_k(Q_0(\varpi)).$$

The claim proposes a complete description of the hyperplanes in the Veronese space associated with a polar space; the source gives no proof, so its status remains open.