User blog comment:Boboris02/Breakthrough! Traditional OCF definition for TON/@comment-30754445-20180414193201/@comment-30118230-20180415085301

+LittlePeng9 Ok, I will correct you on the first paragraph. It's not an older version. It's the C function described in the "Built From Below with Passthrough for Lower Levels" section. The original C, which is the main notation was defined in 2006 while the passthrough C was defined in 2016 so it's actually newer. However, the Passthrough C takes the form $$C_i(\alpha,\beta)$$ which corresponds to $$C(\Omega_2i+\alpha,\beta)$$ in the second system of the main notation, so what has been proven well-founded is bounded by $$C(C(\Omega_2\omega,0),0)$$.