Alive in seki is alive.
threatens to make an eye, requiring (see below).
Neither player wants to play at a or b. If Black plays one of them, White makes a bulky five. If White plays a, Black captures and makes two eyes. If White plays b, Black must capture. White may not recapture if the rules forbid repeating positions, but even if the rules allow it, it's a loss of one point in gote.
I think this position is an example of case S1 at Almost Almost Fill, meaning that the inside shape is a killing shape, and neither of its extensions makes a killing shape. According to that page, the groups in such a position are alive in seki regardless of whose turn it is and the number of external liberties.
If White doesn't play as in the diagram above, Black can live without seki.
unkx80: Yes, this is the solution.
David: Thanks for your help.
demetria: Good job, David! I like your solution, even though I couldn't make mine work :)
Alex: Forgive me for asking, but what happens if black plays like so;
unkx80: Then captures. Next,