You are misrepresenting or more likely have simply misunderstood the Pigeonhole Principle. Which I guess makes sense for somebody who didn't understand why length extension matters. It does not prove that any particular output will recur, and what you've got here is one very particular output.

Again, you need actual examples. Not handwaving, not the unwavering yet entirely unjustified certainty that you're correct, you need examples. And you don't have any.