>"Rather than treating a state carrier XnX_n or computational-basis space as the primitive object to be searched, the framework constructs a class map π:Xn→Cn class-indexed fold invariants, polynomial layers, Cantor complexity coordinates, determinantal degeneracy data, algebraic certificates, Thom encodings, and an invariant rank ρ:Cn→Rn. For every objective admitting the exact factorization

F=Φ∘ρ∘π

representative-level enumeration is mathematically unnecessary: the objective is constant on quotient classes and may be evaluated entirely from the reduced carrier."

So basically, you're creating a Rainbow Hash for Mathematical Objects!

Brilliant idea!

AKA a "Lookup Table", aka a "Database" -- for the properties of Mathematical Objects!

Now, I think this could be worth future research... if we have say, a database of mathematical equations, then my question is, "How many distinct Mathematical properties could be their own attribute, aka their own database table "field" -- for each record?"

The above references such mathematical properties as "class-indexed fold invariants, polynomial layers, Cantor complexity coordinates, determinantal degeneracy data, algebraic certificates, Thom encodings", etc.

But, in the world of pure Math (as opposed to merely cryptography), how many additional properties could be added as Database Fields (or Key/Values, if you prefer KV stores) to each Record?

Which would be dependent on others?

Could such a Database, were it to be created, or attempted to be created, be normalized?

And other questions!

Point is, there's a lot of weird-but-interesting (in a good way!) pure Math ideas here, above and beyond the cryptography aspects!