I'd like to chime in with my take on the "slotting" thing.
A trumpet resonates at a certain set of notes. I think of these notes as the slots. If the horn "slots well" these notes are quite discete. That is, if I try to bend the note, I can't get very far before I stumble up or down to the next harmonic. To wax a little technical, this depends on how high and wide the resoncance peaks are in the frequency response of the trumpet.
Now the size of the resonance peaks drops off as we play higher. In the diagrams in my Backus book, they don't seem to get all that much wider, but they are quite a bit les pronounced as we get up around high G (nomenclature alert! I mean the G above the high C just on top of the staff). They are also getting a lot closer together. These facts manifest themselves as the horn not slotting up as well up high as it does down low. We can compensate by playing louder. However, the fact remains that it takes a lot of control from the player to keep from missing notes up above high E or so.
Now comes what, IMHO, is the really interesting part. If we look at the diagrams in the technical books the peaks (slots) are pretty much gone around high G. So how is it that lead players can make the double C literally pop out?
Well, here is what I think. This is just my opinion. Please don't take this as the last word. Anyway...
If I play up around high G, I can smoothly slide up and down from around F to B-flat over high C. The horn is simply acting as a megaphone as these high notes don't reflect all that well off of the bell barrier. So far the acoustics books make sense. Then with a little more focus I can make the double C pop right out. It clicks in. There is clearly a slot there, though the acoustics book say that there shouldn't be. This has bugged me for a while, but I stumbled across something by accident in dealing with an argument last summer.
I do a lot practicing on a ring visualizer. I figured that without the horn, I should be able to hit a smooth continuum of notes. OOPS! I missed something. As soon as I confine some lip mass in a ring, I have a resonant system. Guess where the fundamental seems to be? For me its right at double C! I can make double C's pop out on a ring visualizer.
IMHO, the slot that we have around double C is by and large brought on by the lip mass, the rim and the mouthpiece. The trumpet isn't supposed to resonante up there.
QUALIFIER!! Now there something that still bugs me. If my little theory is true, I should be able to tell no difference between horns when I play double C's. However, I can. My Shew Horn clearly barks much better than my Benge or my Tanabe Horn (sorry Wayne - FWIW my Tanabe horn is my first choice for legit B-flat work, but I have a tougher time way up there on it). I don't have a good explanation for this. Any ideas?
Going out on a limb here:
I hope I haven't slipped up here with this cursory coverage. Perhaps Chris Stratton could shed some light on this. His technical ideas are always right on.
I'm sure this more than you bargined for.
Thanks for yur patience.