Again, there's enough correlation between ability to perform certain tasks that you don't need an infinite recursion. To test AIv(N+1)'s ability to program to exact specification, instead of having it program AIv(N+2) have it instead program some other things that AIvN finds difficult (but whose solutions are within AIvN's power to verify). That we will be applying AIv(N+1)'s precision programming to itself doesn't mean we can't test it on non-recursive data first.

ETA: Of course, since we want the end result to be a superintelligence, AIvN might also ask AIv(N+1) for verifiable insight into an array of puzzling questions, some of which AIvN can't figure out but suspects are tractable with increased intelligence.