Halliday & Matthiessen (2014: 540):
Other than with 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’, e.g.
Earl Russell says it is inevitable, though profoundly regrettable, [[that the agitation against the Polaris base has generated some antagonism to the policy of the United States]].
In that article, it’s no coincidence [[that I have a big fight with Twain and Eliot]], || because I disagree with them on issues [[that concern all of us]].
Until 1940 it was an observable fact [[that there were composers whose music was highly prized in some countries and entirely neglected by their neighbours]], and this was explained by the difference in national characters.
It is clear [[that the Princess and her husband are settling down in London]] and for this purpose, Kensington Palace is well suited.
The Federal Government has made it clear [[that it would have no part in any project for the development of long-range missiles – which in any case would contravene the provisions of the Brussels treaty]].
The third reason is [[that the supreme interest for the whole world – East and West and uncommitted nations – is the prevention of nuclear war]].
The lesson [[that’s learned]] is [[that they aren’t Kangan]]; Kangan is everybody, as represented by the people gathered in Beatrice’s apartment at the end of the novel. [Text 16]Perhaps the most important point of all is the fact [[that capital was available for expansion as required]].
The plain fact is [[[that it is extremely difficult [[for MPs to accept invitations from foreign Governments, or from public relations organisations [[working for them]] ]], || without being compromised]]].
[identifying clause of proving]
But the fact [[that they are caught]] proves [[that they do not lift above the headline]].
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 (Carrier or Identifier/Token, in these examples).³³ Since it is embedded, there is always an agnate version where the fact clause serves as a Qualifier of a noun of the ‘fact’ class, e.g. the fact that Caesar was ambitious.
³³ Strictly speaking the embedded ‘fact’ clause functions as Head of a nominal group which, in turn, functions as an element in the ranking clause. This analysis shows how clauses serving as Head are agnate with clauses serving as Postmodifier in nominal groups with a fact noun as Head: that Caesar was ambitious is obvious: the fact that Caesar was ambitious is obvious. But since a fact clause functioning as Head takes up the whole of that nominal group we can just as well leave out that stage in the structural analysis and show it as directly embedded into the clause.