This is a new operator I've come up with, which not only grows faster than any conventional hyperoperator (e.g. pentation), but also grows faster than any extended hyperoperator (e.g. megotion). It doesn't fit precisely into the framework thanks to BEAF's weirdness so I can't really express it as the limit of a sequence of other established functions, but it's not too far away and I'm sure I could make a modified version which could fit in with a little fiddling.
It will use the notation:
It is defined as follows, using PRBN:
\[A\circledcirc B = \circledast[A]_B[A](A)\]
The growth rate of
in FGH should be something close to