different definitions of precession parameter "k" between DD and DDGR #1958

while simulating TOAs for a hypothetical relativistic binary system, i found that synthetic, high-precision TOAs created with DDGR produced quasi-periodic residual variations when attempting to instead use a DD model. these variations did not go away even when using spot-on initial guesses for the DD post-Keplerian parameters. after some digging around, i eventually saw that the two models use different definitions of the precession parameter (k):

DDGR definition of k:

def k(self):
    """Precessing rate assuming GR

    Taylor and Weisberg (1989), Eqn. 16
    """
    return self._k

where self._k is the (constant) secular variation defined in the _updatePK() internal method, and

DD definition of k:

def k(self):
    # separate this into a property so it can be calculated correctly in DDGR
    # note that this include self.pb() in the calculation of k
    # and self.pb() is PB + PBDOT*dt, so it can vary slightly
    # compared to a definition that does not include PBDOT
    # I am not certain about how this should be done
    # but this is keeping the behavior consistent
    return self.OMDOT.to(u.rad / u.second) / (2 * np.pi * u.rad / self.pb())

the key difference arises in the use of self.pb() in the DD version; if I instead make the two definitions the same, the quasi-periodic feature goes away and i obtain flat residuals.