Earlier quoted context omitted.
One concurrent insertion, or one network partition. UUIDs can be generated on many machines with no awareness of each other and merged later.
I would recommend reviewing my prior comments on this, as I address the concerns of multiple nodes needing to be able to independently produce identities without collisions or coordination. If you know beforehand the maximum number of participants in your system, you can divide the keyspace across that quantity. If you are using BigInteger or equivalent, you have an infinite number of these things to work with, so it…
A UUID is just a 128-bit integer, with creation algorithms designed to partition that space by things that already have enough entropy to need no further synchronization.
What you're proposing sounds like roll-your-own-UUID, which might be similarly inadvisable as roll-your-own-crypto.