  Inspired by the study of loose cycles in hypergraphs, we define the
\emph{loose core} in hypergraphs as a structure which mirrors the close
relationship between cycles and $2$-cores in graphs. We prove that in the
$r$-uniform binomial random hypergraph $H^r(n,p)$, the order of the loose core
undergoes a phase transition at a certain critical threshold and determine this
order, as well as the number of edges, asymptotically in the subcritical and
supercritical regimes.
  Our main tool is an algorithm called CoreConstruct, which enables us to
analyse a peeling process for the loose core. By analysing this algorithm we
determine the asymptotic degree distribution of vertices in the loose core and
in particular how many vertices and edges the loose core contains. As a
corollary we obtain an improved upper bound on the length of the longest loose
cycle in $H^r(n,p)$.
