Flexible stability conjecture for higher-rank arithmetic lattices

Let $\Gamma$ be the arithmetic group specified by the local-to-global conjecture above. A group $G$ is flexibly stable if every sufficiently accurate approximate homomorphism from $G$ to a symmetric group is uniformly close to a homomorphism into a symmetric group whose degree increases by at most a prescribed relative amount. Flexible stability conjecture. Then $\Gamma$ is flexibly stable. The paper proves flexible stability for a particular spin arithmetic group and presents this assertion as what the local-to-global conjecture would imply for higher-rank lattices; the general statement remains open.