The E2-degeneration conjecture for the symplectic spectral sequence

Let $X$ satisfy the conditions imposed in the first paragraph of the relevant section. Assume in addition that $X$ admits a homological Lagrangian section and that $SH^0(X;\Bbbk)$ is a smooth algebra. Consider the spectral sequence associated with the filtered symplectic complex in the stated theorem.

The E2-degeneration conjecture. The spectral sequence degenerates at the $E_2$ page.

This is motivated by the affine case, where the relevant hypercohomology spectral sequence is represented by a single complex and degenerates at $E_2$. The conjecture predicts the analogous degeneration for the symplectic spectral sequence under the additional Lagrangian-section and smoothness assumptions.