User blog comment:Ecl1psed276/Star Notation Revamped! - Introduction and Analysis/@comment-36984051-20190623191704

Unfortunately, you seem to have missed an anoying ordinal near Gamma 0. The limit of

φ(ω,Γ_0+1), φ(φ(ω,0),Γ_0+1), φ(φ(φ(ω,0),0),Γ_0+1), ... is actually φ(Γ_0, 1) = ψ(Ω^Ω+Ω^(ψ(Ω^Ω))).

After nesting φ(Γ_0,φ(Γ_0,φ(Γ_0,φ(...)))) you get the most annoying ordinal of them all: φ(Γ_0+1, 0) = ψ(Ω^Ω+Ω^(ψ(Ω^Ω)+1)). Look at the analysis of EAN for more of these annoying ordinals.