Yes. The bouncing neutrons can't have zero energy; there's a minimum energy they can have. You see the population of neutrons having that energy with the first jump. The subsequent plateau tells you that there are no other neutrons with a slightly higher energy.
(It's tempting to think of the plateau as representing the first energy level, but that's wrong; remember, it's a plateau in counting rate, not in energy. The first jump represents the first energy level.)
And if so, what is the second level they've found?
The sudden increase of neutrons after the first plateau represents the sudden acceptance of a second population of neutrons having a higher energy. If these neutrons had not a single energy, but a distribution of energies, you'd see the population slowly ramping up with absorber height after the first plateau, but that isn't what's seen. The counting rate jumps up sharply after the first plateau.
And then finally, when Stockholm calls you, will you get me a ticket to the ceremony?
Stockholm keeps calling me, but I won't accept the call as long as they keep reversing the charges!
That's probably Ingrid. She's 23, single, very lonely, and she gets excited discussing cosmology. I gave her your number.