A hologram for pure state AdS black holes

We extend the HKLL holographic smearing function methods to reconstruct local bulk operators in the background of a large AdS black hole formed by null matter collapse a pure state black hole from the underlying CFT which is undergoing a sudden quench In particular we sketch how to probe the near horizon and sub horizon bulk locality in the leading semiclassical limit infinite N and ultimately their non perturbative departure from locality by finite N effects which arise due to restrictions imposed in a