Halliday & Matthiessen (2014: 545):
Table 7-28 summarises the distribution of hypotactic projection of idea and locution clauses in clauses nexuses vs. embedded fact clauses across process types. The table includes both propositions and proposals;
Importantly, note that the table mistakenly presents the 'perceptive' example of projection, (we saw) that the boats had been turned, as a hypotactic report of a clause complex instead of an embedded fact serving as Phenomenon of a single clause. Perceptive mental processes do not project idea clauses into existence. The Phenomenon that is seen here is the state of affairs resulting from a past event. See § 7.4.6 (pp505-6).