User blog comment:Bubby3/BM1 is weaker than expected./@comment-30754445-20180326110100/@comment-30754445-20180326150416

I actually didn't have a specific method in mind. I'm simply saying that you gotta prove the equivalences that you're claiming. There should be no gaps of logic. No jumps which aren't completely self-evident.

What Littlepeng's suggested is probably the safest way to achieve this goal. It could also be done with a table, but only if every step along the way is carefully justified.

I think one of the reasons everybody got it wrong last time, is that we've extrapolated patterns we've noted without properly justifying this extrapolation.

For example, when we got (for BM1):

(0,0)(1,1)(2,1) = ζ₀ = ψ(Ω)

(0,0)(1,1)(2,1)(3,1) = Γ₀ = ψ(Ω↑↑2)

(0,0)(1,1)(2,1)(3,1)(4,1) = LVO = ψ(Ω↑↑3)

We jumped to the conclusion that (0,0)(1,1)(2,1)...(n+1,1) = ψ(Ω↑↑n) without bothering to check whether this extrapolation is warranted. Now, this specific equivalence is probably true. In fact, most of the time this kind of reasoning works fine. But if there's a problem in the notation or even just an unexpected twist, these extrapolations will mislead us. You're practically guaranteed to miss any major issues, when doing the analysis in this manner.