Binary black holes formed via different pathways are predicted to have
distinct spin properties. Measuring these properties with gravitational waves
provides an opportunity to unveil the origins of binary black holes. Recent
work draws conflicting conclusions regarding the spin distribution observed by
LIGO–Virgo–KAGRA (LVK). Some analyses suggest that a fraction of the observed
black-hole spin vectors are significantly misaligned (by $>90^\circ$) relative
to the orbital angular momentum. This has been interpreted to mean that some
binaries in the LVK dataset are assembled dynamically in dense stellar
environments. Other analyses find support for a sub-population of binaries with
negligible spin and no evidence for significantly misaligned spin — a result
consistent with the field formation scenario. In this work, we study the spin
properties of binary black holes in the third LVK gravitational-wave transient
catalog. We find that there is insufficient data to resolve the existence of a
sub-population of binaries with negligible black-hole spin (the presence of
this sub-population is supported by a modest Bayes factor of 1.7). We find
modest support for the existence of mergers with extreme spin tilt angles $>
90^\circ$ (the presence of extreme-tilt binaries is favored by a Bayes factor
of 10.1). Only one thing is clear: at least some of the LVK binaries formed in
the field. At most $89\%$ of binaries are assembled dynamically (99\%
credibility), though, the true branching fraction could be much lower, even

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