Sure, but isn’t the goal of the whole agenda to show that Λdoes have a certain correct factorization, i. e. that abstractions are convergent?
I suppose it may be that any choice of low-level boundaries results in the same Λ, but the Λ itself has a canonical factorization, and going from Λ back to XT reveals the corresponding canonical factorization of XT? And then depending on how close the initial choice of boundaries was to the “correct” one, Λ is easier or harder to compute (or there’s something else about the right choice that makes it nice to use).
Λ is conceptually just the whole bag of abstractions (at a certain scale), unfactored.
Sure, but isn’t the goal of the whole agenda to show that Λ does have a certain correct factorization, i. e. that abstractions are convergent?
I suppose it may be that any choice of low-level boundaries results in the same Λ, but the Λ itself has a canonical factorization, and going from Λ back to XT reveals the corresponding canonical factorization of XT? And then depending on how close the initial choice of boundaries was to the “correct” one, Λ is easier or harder to compute (or there’s something else about the right choice that makes it nice to use).
Yes, there is a story for a canonical factorization of Λ, it’s just separate from the story in this post.