Open vs. Closed Loop

[Improbcat]

I'm trying to clarify something. From what I've read open loop is when the engine is using a default a/f mix, and closed loop is when it is using an a/f mix based on the reading of the O2 sensor and such.

O know the engine runs in open loop until it is warmed up.

Once warmed up should it stay in closed loop or should it be cycling between open and closed depending on throttle, gear, etc?

I ask because I was noticing that Box cycles back and forth, but I have no idea if that is normal or not.