Scale-invariant toy Rota Basis conjecture on circuit-rich pools

Let $n$ be the rank, and consider the circuit-rich pool instances generated by the source's recipe. Scale-invariant toy Rota Basis conjecture. For $n\in\{5,7,9,11,13\}$ and pool size $\lceil2.2n\rceil$, the evolved scale-aware policy succeeds within $O(n^2)$ steps. More ambitiously, there exists a constant $c>2$ such that for every $n\geq5$, on pools of size $\lceil cn\rceil$ generated by the same recipe, a deterministic de-randomization of the policy succeeds. This is a computationally motivated generalization of the finite-rank experiments; neither the all-$n$ assertion nor the required de-randomization is proved in the supplied text.