Conjecture on a split limit mixed Hodge structure at an ideal point

Let $M$ be the relevant hyperbolic three-manifold, let $X=\tilde{X}(M)_0^{\mathrm{sm}}$, and let $P$ be an ideal point of $X$. Choose a local uniformizer $z$ at $P$ with $\tilde{m}(0)=1$, and let $a_1,a_2,b_1,b_2,u(z),v(z),cs(z)$ and $s(z)$ be the quantities occurring in the stated limit mixed Hodge structure. Split-limit conjecture. There exists an ideal point $P$ and such a uniformizer $z$ for which

$$\lim_{z\rightarrow 0}\left((2\pi i)^2 cs(z)+(u(z)-2a_1\log z)v(z)\right)\in\mathbb{Q}\cdot(2\pi i)^2,$$

equivalently,

$$\lim_{z\rightarrow 0}s(z)=\lim_{z\rightarrow 0}\left((2\pi i)^2 cs(z)+(a_2b_1-a_1b_2)\log z-a_1b_1(\log z)^2\right)\in\mathbb{Q}\cdot(2\pi i)^2.$$

In other words, for a suitable parameter, the limit $\mathbb{Q}$-mixed Hodge structure of the CS-VMHS at the tangent vector $\frac{\partial}{\partial z}$ is split:

$$\mathbb{Q}\oplus\mathbb{Q}(1)\oplus\mathbb{Q}(2).$$

This predicts a rationality and splitting property for the limiting Chern–Simons variation at an ideal point of the character variety; the supplied text does not state whether the conjecture is known or open.