Boolean degree 1 classification conjecture for families of lines in polar spaces

Let ${\mathcal P}$ be a rank $d$ polar space, and let $Y$ be a family of lines with characteristic vector $\chi_Y \in \langle \bm{j}\rangle + V_{10} + V_{11}$. Consider the examples consisting of the sets of all lines through a point, all lines in a degenerate hyperplane, or all lines in a nondegenerate hyperplane, together with the operations of taking complements, set differences for nested families, and unions of disjoint families. Boolean degree 1 classification conjecture. There exists a constant $d_0(q)$ such that if $d \geq d_0(q)$, then $Y$ can be obtained by combining these examples with these operations, with $W=V_{10}+V_{11}$. This predicts that, in sufficiently large rank, all Boolean degree 1 functions on lines are generated by the known elementary constructions. The claim is presented as a paraphrase of Conjecture 5.1 in the cited work; no resolution is given here.