TT is used in expressions like this one:

                 +----------MVp---------+               
                 |        +------DG-----+               
		 |        |     +--TT---+-Cs-+
                 |        |     |       |    |
I.p knew.v I.p loved him the first.a time.i I.p saw.v him 

In such cases, "the first time" is really like a conjunction,
connecting two clauses together. The word "time" serves as the
head of the conjunction phrase. ("Day", "moment", and a few 
other words can also serve this function.) The TT connects 
"time" to a previous adjective like "first" or "last". (With
some words, like "next" and "second", NR is used instead.)
The "DG" can only be satisfied by the word "the".