The paper on random generics establishes that the equivalence relation identifying two reals when they generate the same random generic extension is not essentially free. A central open problem emerging from this result is whether this equivalence relation is Borel reducible to isomorphism of countable structures, which would place it within the well-studied hierarchy of classifiable equivalence relations. The difficulty is that the algebraic structure of generic extensions is highly non-explicit and depends on set-theoretic properties that resist direct combinatorial encoding. Current techniques from the theory of turbulence and Hjorth's theory provide lower bound obstructions but do not settle whether a reduction to graph isomorphism or a similar relation exists. Anti-foundation axioms from the second paper add further complexity by allowing non-well-founded extensions that could generate new equivalence relations with entirely different complexity profiles, and the third paper's results on ideals in choice-free settings suggest that the standard Baire category tools used to analyze reducibility may fail in the very models where these equivalence relations are most natural.