Reeh-Schlieder conjecture for the free Dirac field

Let $M$ be a globally hyperbolic spin spacetime and let $O\subset\mathcal{M}$ be a bounded cc-region with non-empty causal complement. Let ${\mathbf{F}}^0$ and ${\mathbf{R}}^0$ denote the locally covariant quantum field theory functor and its state-space functor for the free Dirac field. Reeh-Schlieder conjecture. There is a state $\omega\in{\mathscr{R}}^0$ on ${\mathcal{F}}^0_M$ which has the Reeh-Schlieder property for $O$. The conjecture is motivated by the extension of deformation arguments from spacetimes to spin spacetimes; the proof sketch reduces it to a generalisation of the Reeh-Schlieder deformation theorem using a quasi-free KMS state on an ultrastatic spin spacetime.