Generalized weak Chinburg's conjecture for primitive odd characters

Let $m(R)$ denote the Mahler measure of a non-zero rational function $R$, let $L'(\chi,-n)$ denote the derivative of the Dirichlet $L$-function associated with a character $\chi$, and let $\operatorname{Re}$ denote real part. Generalized weak Chinburg's conjecture. For every primitive odd Dirichlet character $\chi$ of conductor $f$, there exists a non-zero rational function $R_\chi\in\mathbb{Q}(z_1,\ldots,z_{n+1})$ and a rational number $r_\chi$ such that

$$r_\chi m(R_\chi)=2\operatorname{Re}(L'(\chi,-n)).$$

This proposed generalization extends Chinburg's conjecture from odd quadratic characters to all primitive odd Dirichlet characters, motivated by examples from the $P_d$ family. The source does not state whether it has been resolved.