Degeneration of the noncommutative Hodge-to-de Rham spectral sequence

Prove degeneration of the noncommutative Hodge-to-de Rham spectral sequence for smooth and proper d($\mathbb{Z}/2$)g categories.

Background

In the construction of the noncommutative Hodge filtration, the paper assumes that the Hodge-to-de Rham spectral sequence degenerates. Under this assumption, negative cyclic homology forms a vector bundle over the formal disk, allowing the authors to combine it with the Kashiwara–Malgrange V-filtration associated to the regular-singular t-connection.

The paper notes that the analogous degeneration result is known in the $\mathbb{Z}$-graded case through work of Kaledin, but remains unresolved in the $\mathbb{Z}/2$-graded setting. Thus the problem is a prerequisite for obtaining the stated filtration construction without imposing the additional assumption.