Whitney smoothing conjecture for derived manifolds

Let $l\geq k>0$, fix an o-minimal structure, and let a derived $C^k$-manifold be a manifold in the corresponding derived differentiable setting. Whitney smoothing conjecture. Every derived $C^k$-manifold is $C^k$-diffeomorphic to a derived $C^l$-manifold, and this derived $C^l$-manifold is unique up to $C^l$-diffeomorphism. This is the derived analogue of smoothing and uniqueness results for ordinary manifolds; the source presents it among conjectural extensions of Whitney's theorems and does not establish it.