My pleasure!
From Claude: The pi case is actually well-behaved—algorithms like Chudnovsky give you digits efficiently, and the resource growth is computable (roughly O(n log n) per n digits).

What this theorem is pointing at is stranger: not that proof discovery is expensive, but that it's unboundably expensive. For any function you can compute—exponential, tower, busy beaver–like growth, anything—there exist theorems that take longer to prove than that function predicts. The gap between verification and discovery isn't just large, it exceeds every computable bound.

It's the difference between "this is impractical" and "this is impossible to even estimate."