Timing six energetic rotation-powered X-ray pulsars, including the fast-spinning young PSR J0058-7218 and Big Glitcher PSR J0537-6910

Measuring a pulsar's rotational evolution is crucial to understanding the nature of the pulsar. Here we provide updated timing models for the rotational evolution of six pulsars, five of which are rotation phase-connected using primarily NICER X-ray data. For the newly-discovered fast energetic young pulsar, PSR J0058-7218, we increase the baseline of its timing model from 1.4 days to 8 months and not only measure more precisely its spin-down rate nudot = (-6.2324+/-0.0001)x10^-11 Hz s^-1 but also for the first time the second time derivative of spin rate nuddot = (4.2+/-0.2)x10^-21 Hz s^-2. For the fastest and most energetic young pulsar, PSR J0537-6910 (with 16 ms spin period), we detect 4 more glitches, for a total of 15 glitches over 4.5 years of NICER monitoring, and show that its spin-down behavior continues to set this pulsar apart from all others, including a long-term braking index n = -1.234+/-0.009 and interglitch braking indices that asymptote to