Grand Unity Conjecture

[andydude]

has Cauchy tetration been (dis)proven to be equivalent to kneser tetration ?

No proof. One of the reasons why we list these as separate methods is that we don't know for sure if they are equivalent. If we could prove that two methods are equivalent, then we would list them as a single method.

is Andrew's slog = carleman ?

No proof. However, there is strong numerical evidence to indicate that they are equal. Procedurally, intuitive Abel iteration and Carleman matrix iteration are very different. Granted, they are both matrix methods, but the first uses matrix inverse, while the second uses matrix power, which is why they cannot be compared directly.