  We study the typical structure of a sparse Erd\H{o}s--R\'enyi random graph
conditioned on the lower tail subgraph count event. We show that in certain
regimes, a typical graph sampled from the conditional distribution resembles
the entropy minimizer of the mean field approximation in the sense of both
subgraph counts and cut norm. The main ingredients are an adaptation of an
entropy increment scheme of Kozma and Samotij, and a new stability for the
solution of the associated entropy variational problem. Our proof suggests a
more general framework for establishing typical behavior statements when the
objects of interest can be encoded in a hypergraph satisfying mild degree
conditions.
