  We establish resolution bounds on reconstructing a bulk field from boundary
data on a timelike hypersurface. If the bulk only supports propagating modes,
reconstruction is complete. If the bulk also supports evanescent modes, local
reconstruction is not achievable unless one has exponential precision in
knowledge of the boundary data. Without exponential precision, for a Minkowski
bulk, one can reconstruct a spatially coarse-grained bulk field, but only out
to a depth set by the coarse-graining scale. For an asymptotically AdS bulk,
reconstruction is limited to a spatial coarse-graining proper distance set by
the AdS scale. AdS black holes admit evanescent modes. We study the resolution
bound in the large AdS black hole background and provide a dual CFT
interpretation. Our results demonstrate that, if there is a black hole of any
size in the bulk, then sub-AdS bulk locality is no longer well-encoded in
boundary data in terms of local CFT operators. Specifically, in order to probe
the bulk on sub-AdS scales using only boundary data in terms of local
operators, one must either have such data to exponential precision or make
further assumptions about the bulk state.
