  In a recent landmark paper, Khoa L\^e (2020) established a stochastic sewing
lemma which since has found many applications in stochastic analysis. He
further conjectured that a similar result may hold in the context of the
reconstruction theorem within Hairer's regularity structures. The purpose of
this article is to provide such a stochastic reconstruction theorem. We also
discuss two variations of this theorem, motivated by different constructions of
stochastic integration against white noise. Our formulation makes use of the
distributional viewpoint of Caravenna--Zambotti (2021).
