  The understanding of neutron star equation of state hinges on a comprehensive
analysis of multi-messenger, multi-wavelength data. The recent scrutiny of PSR
J0030+0451 data by NICER introduces complexities, unveiling a tension with
another X-ray observation of the central compact object in HESS J1731-347,
specifically concerning the mass-radius constraint of low-mass neutron stars.
This tension persists when integrating NICER's updated data with LIGO/Virgo's
gravitational-wave data from the GW170817 binary neutron star merger. Despite
attempts to reconcile these disparate observations, the current combined data
still can not distinguish different types of neutron stars -- whether they are
pure neutron stars or hybrid stars. Bayesian inference indicates only modest
changes in the posterior ranges of parameters related to the nuclear matter and
deconfinement phase transition. This ongoing exploration underscores the
intricate challenges in precisely characterizing neutron stars. It also points
out that it is possible to probe the equation of state at different density
regimes from future more accurate radii of neutron stars with various masses.
