The Catastrophe Theory is an opinion held by some agents of the PPC that HQ is headed for imminent destruction. By looking at the increasing frequency of PPC Emergencies, they have concluded that The End Is Nigh. They even have a graph to demonstrate that fact:
A later version of the theory, adopted after the moratorium on Emergencies meant several years passed without the dreaded Catastrophe occurring, posits that DOOM is actually already here:
No one is quite sure what to make of this. As it stands, the current status and popularity of the Catastrophe Theory within the PPC are unknown, but knowing how askew one's perception of reality can become in HQ, there's probably still someone who is convinced of its validity.
Catastrophe Theory is not particularly related to Cycle Theory, although many of the same people believe in both, and some say that the latter may be a cause of the former.