Halliday & Matthiessen (2004: 472, 473, 474):
Other than impersonals such as it is said, it is rumoured, it seems, the typical environment for a fact is a ‘relational’ process clause of the ‘intensive’ type, either ‘attributive’ or ‘identifying’ … Here the fact is an embedded clause standing as a nominalisation on its own, functioning as the realisation of an element in the relational process clause … Since it is embedded, there is always an agnate version where the fact clause serves as Qualifier of a noun of the ‘fact’ class, for example the fact that Cæsar was ambitious.