Time for another computable function!
The VAST function (notated E[a](n), with a being an ordinal) is a two-variable computable extension to Plexation, that is immensely stronger than most computable functions, if not all of them, to date.
VAST function stands for Very-Awesome-Super-Tremendous function, and is called so based of the principle of yolo.
Definition is simple:
Base rule: E0(n) = )n( (Plexation)
Successor rule: Ea+1(n) = Ea(n)<0<P(n)<1>>1> (Using TaN)
Limit rule: Ea(n) = Ea[Ea[n](n)](n) If and only if a is a limit ordinal.
Salvation rule: m+1E0(n) = mE(FOOST(10^n))(n)
Rule rule: 0E(n) = E(FOOST(10^n))(n)
Obviously, this function is comparable to the FGH itself, and so keeps up with it as long as limit ordinals are defined, making it meaningfully strong.
Hyperkthulhu = EΨ(ψᵢ(0))(5,000)
Quite big, if I may say so myself.
Extension into a one-variable, uncomputable function
Define an alternate version of Rayo(n) (We'll call it FOOST(n)), which instead of generating the largest finite number with n symbols, will generate the largest recursive ordinal and a system of fundamental sequences that goes up to that ordinal and covers all smaller ordinals (An ordinal is considered recursive iff it is the order type of a computable well-ordering of a subset of the natural numbers).
E(n) = E(FOOST(10^n))(n)
Ultrakthulhu = E(5,000)
Calculating a couple of examples
E1(2) = E0(2)<0<P(n)<1>>1> = )2(<0<P(n)<1>>1> (Pretty big)
E2(2) = E1(2)<0<P(n)<1>>1> (Bigger)