576-periodicity conjecture for free fermion conformal nets

Let $\mathit{Fer}(n)$ denote the conformal net of $n$ free fermions, and let $\mathit{CN}$ denote the 3-category of conformal nets, with its notion of $\mathit{CN}$-equivalence. For every integer $n$, the 576-periodicity conjecture asserts that there exists a $\mathit{CN}$-equivalence between

$$\mathit{Fer}(n)\quad\text{and}\quad\mathit{Fer}(n+576).$$

The conjecture proposes a conformal-net analogue of the 8-fold Morita periodicity of real Clifford algebras and of the 576-periodicity of topological modular forms. The corresponding algebraic periodicity for free fermion nets had not been established in the source.