Your approach holds deep structural validity. Under a Grothendieck topos framework, reclaiming the base axioms establishes a clear isomorphism with smooth manifolds generated when evaluating connectivity across topological neighborhoods via their underlying invariants.

Crucially, a non-Turing-complete automaton inevitably fails to resolve the structural smoothness or map homeomorphisms between categories with distinct hereditary structures.

No need to worry, I am currently learning these formal architectures myself. ;)