  Nuclear theory and experiments, alongside astrophysical observations,
constrain the equation of state (EOS) of supranuclear-dense matter. Conversely,
knowledge of the EOS allows an improved interpretation of nuclear or
astrophysical data. In this article, we use several established constraints on
the EOS and the new NICER measurement of PSR J0437-4715 to comment on the
nature of the primary companion in GW230529 and the companion of PSR
J0514-4002E. We find that, with a probability of $\gtrsim 84\%$ and $\gtrsim
68\%$, respectively, both objects are black holes. These likelihoods increase
to above $95\%$ when one uses GW170817's remnant as an upper limit on the TOV
mass. We also demonstrate that the current knowledge of the EOS substantially
disfavors high masses and radii for PSR J0030+0451, inferred recently when
combining NICER with XMM-Newton background data and using particular hot-spot
models. Finally, we also use our obtained EOS knowledge to comment on
measurements of the nuclear symmetry energy, finding that the large value
predicted by the PREX-II measurement displays some mild tension with other
constraints on the EOS.
