Does Killy Find the Net Terminal Gene?

Killy does, indeed, find the Net Terminal Gene, which has been recreated in a manner that's wholly consistent with the series' transhumanist ideals. However, it's unclear how, exactly, it'll stop the City's growth.

Who has the Net Terminal Gene?

Kyrii is a main character of Blame!. He is a cyborg tasked by the governing AI agency with finding a human in the 5.3-AU radius Megastructure who still possesses the Net Terminal Gene, a genetic marker necessary for safe access to the Netsphere, from which the functions of the Megastructure may be controlled.

Why is Killy looking for the net terminal gene?

At some point, the Administration used what limited power they had to create a provisional Safeguard unit in the form of Killy. They tasked him with finding a living Net Terminal Gene carrier with the intent of re-subjugating the City to humanity's control.