Halliday & Matthiessen (2014: 542):
However, we also need to take note of ‘attributive’ clauses where the Carrier is realised by a nominal group denoting a person and the Attribute is a nominal group with an embedded fact clause, either ‘possessive’ with a noun as Head (e.g. idea, notion, inkling [[that ...]]) or ‘intensive’ with an adjective as Head of the nominal group (e.g. sure, certain, aware, cognisant, oblivious (of the fact) [[that ...]]); for example:
They would have no idea [[[that the current British theatrical renaissance is having an effect far beyond the West End of London, || so that Broadway is heavily influenced by the highly successful plays of today [[that it has imported from Britain]] ]]].
However, I am not sure [[that [[what probabilists and what physicists mean here by ‘fields’ ]] are quite synonymous]].
These ‘personal’ ‘attributive’ clauses are closely agnate with projecting ‘mental’ clauses: they have no idea ~ they don’t know, I’m not sure ~ I don’t know.