The higher smooth homotopy hypothesis for Lie n-algebroids and Lie n-groupoids

Let Lie $n$-algebroids and Lie $n$-groupoids be equipped with $n$-equivalences and equivalences, respectively. A source $n$-connected Lie $n$-groupoid is one whose source fibers satisfy the source $n$-connectedness condition proposed in the source.

Higher smooth homotopy hypothesis. Lie $n$-algebroids up to $n$-equivalence are equivalent to source $n$-connected Lie $n$-groupoids up to equivalence. In particular, generalized $n$-morphisms of Lie $n$-algebroids integrate to generalized $n$-morphisms of Lie $n$-groupoids.

The source explicitly leaves the meaning of source $n$-connectedness vague and notes that a more general notion of Lie groupoid may be needed because of the failure of Lie's third theorem. The conjecture is therefore open and technically provisional.