The integer-finite local-system conjecture in intersection K-theory

Let $f:X\to S$ be a surjective map of relative dimension $d$, with $X$ smooth. Let $U$ be a smooth open subset of $S$ such that $f^{-1}(U)\to U$ is smooth. For $y\in U$, let $\pi_1(U,y)$ act on the irreducible components of top dimension of $f^{-1}(y)$, and let $L$ be the associated local system. An integer finite local system is a local system arising from this action with finite monodromy on an integral lattice.

Integer-finite local-system conjecture. Then $L$ is an integer finite local system, and there is an isomorphism

$$\frac{\textbf{P}^{\leqslant -d}_f\operatorname{gr}^j K_\cdot(X)_\mathbb{Q}}{\widetilde{\textbf{P}}^{\leqslant -d}_f\operatorname{gr}^j K_\cdot(X)_\mathbb{Q}}\cong \operatorname{gr}^j\textbf{I}K_\cdot(S,L)_\mathbb{Q}.$$

This statement extends the proposed semismall decomposition picture to surjective maps of arbitrary relative dimension. The supplied text does not give evidence of a resolution, so the claim remains open.