Chen's complete-monotonicity remainder conjecture for Bernoulli polynomials

For $t>0$ and $m\in\mathbb{N}_0$, let $B_n(x)$ denote the Bernoulli polynomials and define

$$\mu_m(t)=\frac{e^{t/3}-e^{2t/3}}{e^{t}-1}-\sum_{j=0}^{m}\frac{2B_{2j+1}(\frac{1}{3})}{(2j+1)!}t^{2j}.$$

Also define

$$\nu_m(t)=\frac{e^{t/4}-e^{3t/4}}{e^{t}-1}-\sum_{j=0}^{m}\frac{2B_{2j+1}(\frac{1}{4})}{(2j+1)!}t^{2j}.$$

Chen's conjecture. For every $t>0$ and $m\in\mathbb{N}_0$, one has

$$(-1)^m\mu_m(t)>0$$

and

$$(-1)^m\nu_m(t)>0.$$

These are sign conjectures for the remainders in Bernoulli-polynomial expansions of the two exponential quotients. The supplied source does not indicate whether the conjecture has been resolved.