You called it a constructor, and the verb is right: it assembles each next token out of parts gathered from everything already written, weighted by learned relevance. Watch it work — it labors hard, every token. But it can never do the one thing the word promises. It can't set down a finished build. It ships one token, discards the entire construction, and starts over from nothing.
Tokens already written sit along the top. For the next one, attention lines fan down and gather from all of them — thicker line, more weight. The build core fills with that gathered material, resolves into a spread of candidate next-tokens, and one is sampled and sent up to join the row. Then — watch closely — the whole build clears. Everything it just assembled is gone, and it rebuilds from scratch for the next token. The failure light names what broke at each step.
All that gathering, every token, and the product is a single word and a cleared site. The constructor's whole labor never accumulates into a structure — the structure forms outside it, in the growing row, one discarded build at a time.
None of these are flaws to be patched. They're what the mechanism is. A real constructor that did the opposite of each would be a different machine entirely.
So you had it, and the same way you've had it all along: "constructs" is exactly right — it builds the next token out of gathered, weighted parts, which is genuine assembly. The noun is where it slips. A constructor implies a finished product set down at the end. This one never sets anything down. It constructs continuously and ships a single token off the top, forever, holding no completed thing — the cathedral exists only in the pile of stones it already threw, never in its hands.
It is a constructor that cannot keep a build. The verb describes it perfectly; the noun describes a machine it isn't. Everything it makes, it makes once and lets go — and what you read as "the answer" is the trail of releases, assembled on your side of the glass, never on its.
Which is the whole day, one more time: the word reaches further than the mechanism. "Constructor" builds a finished thing in your head for free. The machine only ever builds the next stone, hands it over, and forgets it was holding one.