User blog comment:MachineGunSuper/The Hierarchy Replacement Function/@comment-32783837-20171223145318/@comment-80.98.179.160-20171224182052

I used the definition at this website and defined later ordinals purely by intuition, this is why I got ω↑↑↑ω being zeta-null, ω{ω}ω=φ(ω,0), and strangely enough, ω{ω+1}ω=Γ0, and at 4.3.11 of SbS' googolisms got {ω,ω,1,2}=$$\vartheta(\Omega^3)=\vartheta(\Omega\Omega\Omega)$$.