Now it is supposedly disproven by a computer program.

Hardly. The program can only give suggestions as to what is going on behind the actual pressure traces.

I'll (try to) close with my original and unanswered question: how was it established that burn out comes near peak pressure? If someone will cite a reference by the real experts, I'll seek it out. My thermo professor did research in this field for the army, so the library there should contain many works on internal ballistics. Frankly, until this discussion, I'd never considered what happens near peak pressure, and I still haven't a definitive answer.