leaker, d(users)/dt can be negative without bannings.
d(users)/dt is growth in users, not their number. To illustrate: if 600 users registered in February, then only 400 in March HN's growth would be negative; d(users)/dt would be negative.
d(users)/dt would be the rate of change of users. That can only be negative if the amount of users decreases, ie through bannings.
You're thinking of the second derivative, d^2(users)/dt^2, which is the rate of change of the rate of increase of users. If that is negative, it means that the growth has slowed down, as in your example with February and March.
I was asking about the second derivative; if d(users)/dt wasn't constant, then d^2(users)/dt2 is nonzero and eternal september risk is fairly high (assuming HN isn't shrinking). If you assume idealized user growth (which doesn't happen -- there are so many people in the end that would care to either join HN or troll HN), then eternal september is actually guaranteed if d^2(users)/dt2 > 0, since there will come a time t when (new users) > (old users).
d(users)/dt is growth in users, not their number. To illustrate: if 600 users registered in February, then only 400 in March HN's growth would be negative; d(users)/dt would be negative.