Is there a gap between neutron star and black hole masses?
In plain words
Few compact objects have been found between about 2.5 and 5 solar masses, possibly because supernovae rarely make them.
Precise statement
Determine whether the compact-object mass function has a real deficit between $\sim 2.5$ and $\sim 5\,M_{\mathrm{sun}}$, as X-ray binary samples suggest, or whether it is a selection effect, using gravitational-wave events (GW190814 secondary $\sim 2.6\,M_{\mathrm{sun}}$, GW230529 primary $\sim 2.5\ \text{to}\ 4.5\,M_{\mathrm{sun}}$), microlensing and Gaia astrometric binaries. Answer: the depth of the gap as a rate-density ratio with credible interval.
What would settle it
Population inference on gravitational-wave and astrometric samples with selection effects modeled, giving the rate density inside versus outside the gap.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
2024: GW230529 contained an object of $2.5\ \text{to}\ 4.5\ M_{\mathrm{sun}}$ inside the putative gap, suggesting the gap is at most partly empty.
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