Oh, I see what you're driving at! OK. Deep breath. Let's see whether I can make this clear.
Imagine that you and I are standing at the end of a long hallway. I'm throwing superballs at you, and you're catching them. Whenever you catch one, you count it.
Our game is fraught with problems, however. One problem is that I throw like a girl. Sometimes I throw things straight up, and sometimes I throw things straight ahead. Another problem is that the ceiling is very sticky. Whenever a superball hits the ceiling, it gets stuck and it never makes it to you. Fortunately, you can move the ceiling up and down.
If you could see the superballs bouncing, you'd notice that they always seem to bounce to certain specific heights. But you can't see the superballs. All you know is how many I throw, how many you catch, and how high the ceiling is.
If the ceiling is too low, none of the balls make it through. That's because no matter how I through the balls, they always bounce to at least a certain height. You move the ceiling a bit higher, and still see nothing. A bit higher, still nothing, and so on, until you put the ceiling high enough to let the least-bouncy balls through.
Suddenly, you are counting a significant number of balls. "OK," you think, "since I believe the balls can have any old energy above the minimum, I expect that there will be some more balls bouncing only a little bit higher than the minimum. I'll raise the ceiling a little bit, and I'll catch a few more of the balls." So you raise the ceiling a bit, but you still see balls coming down the hallway at the same rate. So you raise it a bit more; still you get the same result. So you raise it more and more, and you realize that the rate at which balls make it down the hall has plateaued as a function of ceiling height.
Then you raise it a bit more. Suddenly, the rate of the superballs makes another big jump! This is because you're suddenly admitting the next energy level: the ceiling has been raised higher than the fixed height to which balls of this energy can bounce.
In the case of the experiment (which uses neutrons instead of superballs, a neutron absorber instead of a sticky ceiling, and a neutron detector instead of a fancy West-coast lawyer), they clearly resolve the first jump, the plateau, and the second jump. There is weak evidence for a second and a third plateau, but the finite resolution of the detector washes them out. But I'd say that they have two discrete energy levels firmly in hand.
"through" = throw