  We have used the Arecibo Telescope to carry out one of the deepest-ever
integrations in radio astronomy, targetting the redshifted conjugate satellite
OH 18 cm lines at $z \approx 0.247$ towards PKS1413+135. The satellite OH 1720
and 1612 MHz lines are respectively in emission and absorption, with exactly
the same line shapes due to population inversion in the OH ground state levels.
Since the 1720 and 1612 MHz line rest frequencies have different dependences on
the fine structure constant $\alpha$ and the proton-electron mass ratio $\mu$,
a comparison between their measured redshifts allows one to probe changes in
$\alpha$ and $\mu$ with cosmological time. In the case of conjugate satellite
OH 18 cm lines, the predicted perfect cancellation of the sum of the line
optical depths provides a strong test for the presence of systematic effects
that might limit their use in probing fundamental constant evolution. A
non-parametric analysis of our new Arecibo data yields $\left[\Delta X/X
\right] = (+0.97 \pm 1.52) \times 10^{-6}$, where $X \equiv \mu \alpha^2$.
Combining this with our earlier results from the Arecibo Telescope and the
Westerbork Synthesis Radio Telescope, we obtain $\left[\Delta X/X \right] =
(-1.0 \pm 1.3) \times 10^{-6}$, consistent with no changes in the quantity $\mu
\alpha^2$ over the last 2.9~Gyr. This is the most stringent present constraint
on fractional changes in $\mu \alpha^2$ from astronomical spectroscopy, and
with no evidence for systematic effects.
