Trifautx (Water's Other Number)

We will be starting this page from the end of the last number, where we defined \hbar(1) as Water's Number. As per tradition, we will go even further and develop and even more extended version of Ackermann numbers. 
Though I won't be doing a repeat of the last number but with \hbar(n), there will be some differences. This extension will start the same way that the original did, as it doesn't change until stacks.
\hbar^2(n) = \hbar(\hbar(n))
\hbar^{\hbar(x)}(y)
\hbar^{\hbar^{\hbar(x)}}(y)
This is where the extension changes.
\hbar[3]x,y = \hbar^{\hbar^{\hbar(x)}}(y)
(Note: Alternatively you can just use n instead of x,y to define both x and y.)
Now the extension mainly takes inspiration from array notations like BEAF or BAN.
\hbar[\hbar[\hbar[\hbar[10^{24}]]]]10 can be compressed into \hbar[[4, 10^{24}]]10.
\hbar[[10^{10},[[10^{10}, 10^{10}]]]]10 can be even further compressed into \hbar\{10^{10},[3]\}10
I know I didn't develop this extension as much as I did the original extension, but I believe this is already large enough of a jump.
I will define Trifautx as \hbar\{\hbar[[10^{10^{100}},\hbar(100)]]10^{24},[\hbar[[300^{600},\hbar(100)]]]3 \uparrow \uparrow \uparrow 10\}10^{10^{10^{100}}}
The symbol is \mu(n), and once again, n is how many times you want it to repeat. No, I'm not guaranteed making ANOTHER extension, but anyway, \mu(1) is default. This concludes Trifautx!
Category:Number