Exponential analyticity-shrinkage conjecture for small perturbations of AdS3

Let $\operatorname{AdS}_3$ denote three-dimensional Anti-de Sitter space, and consider small smooth perturbations whose spatial dependence admits a radius of analyticity $\rho(t)$, defined as the distance from the real spatial axis to the nearest complex singularity of the analytically continued solution. Exponential analyticity-shrinkage conjecture. Small smooth perturbations of $\operatorname{AdS}_3$ remain smooth for all times, but their radius of analyticity shrinks to zero exponentially fast. This conclusion is based on numerical analyticity-strip analysis: the perturbations are observed to remain smooth while increasingly fine spatial scales develop. A rigorous proof of global smoothness and exponential decay of the analyticity radius remains open.