User blog comment:MachineGunSuper/The Hypersonic Triangle Array Notation (REAL final notation)/@comment-30754445-20181118010314

You haven't actually defined anything beyond A*A (which corresponds to ω2).

And you've started with the A's after doing everything from the previous blog post twice, so your grand total is up to:

(ω3+ω2)+(ω3+ω2)+ω2

Which gets you to:

ω3*2+ω2*2

(not, as you might expect, ω3*2+ω2*3. Ordinal addition works a bit differently than ordinary addition)

Oh, and a fair warning:

The point of inventing notations is to define everything yourself. You aren't going to get any achievement points for saying "oh, and from here on it works like the FGH".