Flatness conjecture for the relative connection

Let $F:\mathcal{C}\rightarrow\mathcal{D}$ be an $A_\infty$-functor, and let $HC^-_*(F)$ be its relative cyclic homology equipped with the relative connection $\nabla^F$. Relative connection flatness conjecture. The relative connection is flat, thus endowing $HC^-_*(F)$ with a T-structure. Establishing this would provide the expected T-structure on relative cyclic homology, but the source presents it only as an expectation.