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Mouffles Monster (so named by Sbiis Saibian) is cgG64(G64).[1] It is the 20th record setting entry in the "My number is bigger!" competition.[2] It is defined using the cg(x) function defined by Conway and Guy using chained arrow notation:

$$cg(1) = 1$$
$$cg(2) = 2 \rightarrow 2$$
$$cg(3) = 3 \rightarrow 3 \rightarrow 3$$
and in general
$$cg(n) = n \rightarrow n \rightarrow n \rightarrow . . . \rightarrow n \rightarrow n \rightarrow n$$ with $$n$$ $$n$$'s

Mouffles Monster = cgGraham's Number(Graham's Number) - the exponent indicates iteration of the cg function.