User blog comment:Hyp cos/TON, stable ordinals, and my array notation/@comment-31580368-20191108115404/@comment-11227630-20191108134226

C(Ω2+C(Ω2×2,0),0) is standard because Ω2×2 is 1-built from below from that term so Ω2+C(Ω2×2,0) is 2-built from below from that term. But in C(Ω2+C(Ω2×2+C(Ω2×3,0),0),0), Ω2×3 is not 0-built, Ω2×2+C(Ω2×3,0) is not 1-built, Ω2+C(Ω2×2+C(Ω2×3,0),0) is not 2-built from below from it - the built-from-below condition do not allow Ω2+C(Ω2×2+C(Ω2×3,0),0) < Ω2×2+C(Ω2×3,0) < Ω2×3 like this.

For the same reason, C(Ω2+C(Ω2×C(Ω22,0),0),0) is not standard, because Ω2+C(Ω2×C(Ω22,0),0) < Ω2×C(Ω22,0) < Ω22 as before.