  We fit the high resolution \textit{Chandra} X-ray spectra of the O supergiant
$\zeta$ Puppis using the variable boundary condition (VBC) line model to test
the stability of its mass-loss rate between two epochs of observation: 2000
March and 2018 July -- 2019 August. At issue is whether the observed variations
are induced by global changes in the cool (unshocked) wind itself or are
isolated to the local pockets of hot gas (i.e., changes in the frequency and
location of the shocks). Evidence in the literature favored the possibility of
a 40 per cent increase in the mass flux of the entire stellar wind, based on
X-ray reabsorption from a line-deshadowing-instability-inspired
parameterization, whereas our fit parameters are consistent with a constant
mass flux with a change in the velocity variations that determine the locations
where shocks form. Our results suggest the shocks in the more recent data are
formed at somewhat larger radii, mimicking the enhanced blueshifts and
increased line fluxes interpreted in the previous analysis as being due to
increases in both the X-ray generation and reabsorption from an overall
stronger wind.
