User blog comment:Ubersketch/Homomorphism between Cantor's normal form of finite degree and primitive sequence system/@comment-35470197-20190809223713

The correspondence has already been written in the article of PrSS.

> A homomorphism is a function F between notations A to B such that for all functions f and g in A and all objects a in A, F(f+g(a))=F(f(a))+F(g(a))

Then your correspondence is not a homomorphism, because
 * 1) you have not defined the sum of functions in CNF in your sense.
 * 2) you have not defined addition for PrSS.

> It appears that constructing homomorphisms between ordinal notations provides a promising new easy way of doing analysis without being informal,

It is not new at all. People do so if they do. The point is that there is no ordinal notation suitable for BMS. I am certain that you do not have an ordinal notation even for PSS for which you can easily describe the correspondence.