Slow and steady: long-term evolution of the 76-second pulsar J0901$-$4046

Abstract: PSR J0901$-$4046, a likely radio-loud neutron star with a period of 75.88 seconds, challenges conventional models of neutron star radio emission. Here, we showcase results from 46 hours of follow-up observations of PSR J0901$-$4046 using the MeerKAT, Murriyang, GMRT, and MWA radio telescopes. We demonstrate the intriguing stability of the source's timing solution over more than three years, leading to an RMS arrival-time uncertainty of just $\sim$10$^{-4}$ of the rotation period. Furthermore, non-detection below 500 MHz may indicate a low-frequency turnover in the source's spectrum, while no secular decline in the flux density of the source over time, as was apparent from previous observations, has been observed. Using high time-resolution MeerKAT data, we demonstrate two distinct quasi-periodic oscillation modes present in single pulses, with characteristic time scales of 73 ms and 21 ms. We also observe a statistically significant change in the relative prevalence of distinct pulse morphologies compared to previous observations, possibly indicating a shift in the magnetospheric composition over time. Finally, we show that the W$_{50}$ pulse width is nearly constant from 544-4032 MHz, consistent with zero radius-to-frequency mapping. The very short duty cycle ($\sim$1.4$^{\circ}$) is more similar to radio pulsars with periods $>$5 seconds than to radio-loud magnetars. This, along with the lack of magnetar-like outbursts or timing glitches, complicates the identification of the source with ultra-long period magnetar models.