Relative orthogonal Grassmannian decomposition conjecture for quadric fibrations

Let $p:\mathfrak{Q}\to S$ be a quadric fibration of relative dimension $n+1$ over a smooth base, with fibers $\mathfrak{Q}_s$ of rank at least $4$, where $n$ is odd. Let $\mathcal{C}l_0$ be the sheaf of even Clifford algebras associated with the quadric fibration. Relative orthogonal Grassmannian conjecture. There exists a semiorthogonal decomposition

$$\mathrm{D}^{\mathrm{b}}(\operatorname{OGr}(2,\mathfrak{Q}))=\left\langle\underbrace{\mathrm{D}^{\mathrm{b}}(S,\mathcal{C}l_0),\dots,\mathrm{D}^{\mathrm{b}}(S,\mathcal{C}l_0)}_{n+1\text{ times}},\underbrace{\mathrm{D}^{\mathrm{b}}(S),\dots,\mathrm{D}^{\mathrm{b}}(S)}_{\frac{(n-1)(n+1)}{2}\text{ times}}\right\rangle,$$

where $\mathrm{D}^{\mathrm{b}}(S,\mathcal{C}l_0)$ is the derived category of the sheaf of even Clifford algebras over $S$. This is presented as a natural generalization of the pencil-of-quadrics conjecture to arbitrary quadric fibrations, under a rank condition ensuring flatness. Its resolution status is not specified in the supplied text.