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Measuring a pulsar's rotational evolution is crucial to understanding thenature of the pulsar. Here we provide updated timing models for the rotationalevolution of six pulsars, five of which are rotation phase-connected usingprimarily NICER X-ray data. For the newly-discovered fast energetic youngpulsar, PSR J0058-7218, we increase the baseline of its timing model from 1.4days 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 timederivative of spin rate nuddot = (4.2+/-0.2)x10^-21 Hz s^-2. For the fastestand most energetic young pulsar, PSR J0537-6910 (with 16 ms spin period), wedetect 4 more glitches, for a total of 15 glitches over 4.5 years of NICERmonitoring, and show that its spin-down behavior continues to set this pulsarapart from all others, including a long-term braking index n = -1.234+/-0.009and interglitch braking indices that asymptote to <~ 7 for long times after aglitch. For PSR J1101-6101, we measure a much more accurate spin-down rate thatagrees with a previous value measured without phase-connection. For PSRJ1412+7922 (also known as Calvera), we extend the baseline of its timing modelfrom our previous 1-year model to 4.4 years, and for PSR J1849-0001, we extendthe baseline from 1.5 years to 4.7 years. We also present a long-term timingmodel of the energetic pulsar, PSR J1813-1749, by fitting previous radio andX-ray spin frequencies from 2009-2019 and new ones measured here using 2018NuSTAR and 2021 Chandra data.

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