User blog comment:Tetramur/Pentational arrays and beyond - comparisons/@comment-37993808-20200108154849/@comment-35470197-20200109093117

@Plain'N'Simple

Then my metaphor on the difference of n→f_{ω↑↑ω}(n) and n→f_{n↑↑n}(n) might not be far from the situation.

Could you guess which one fits the OP's analysis table for BEAF-BSC, Bowers' intended one and Saibian's alternative one? As n→f_{ω↑↑ω}(n) and n→f_{n↑↑n}(n) have completely different growth rate, those two behaviours should have completely different growth rate. At least, I guess that the OP states that Bowers' intended one satisfies the single-step conversion X^^^X→p^^^p which looks intuitively very weak, while the OP states that Bowers' intended one belongs to BEAF-BSC. It should imply that Bowers' method fits the table. But... is it so strong that X^^^X corresponds to Γ_0?