Research note
Verification cost explains most of the capability distribution
Where checking an answer is cheap, systems improve fast. Where it is expensive, they do not.
If you plot capability improvement between 2024 and 2026 against almost any property of a task domain, you get noise. Plot it against the cost of verifying whether an answer is correct, and the pattern is close to monotone.
Formal mathematics: verification is a proof check, essentially free. Large improvement. Competitive programming: verification is a test suite, nearly free. Large improvement. Code transformation: verification is compilation plus tests, cheap. Large improvement. Scientific literature synthesis: verification requires a domain expert reading sources, expensive. Moderate improvement. Long-horizon autonomous operation: verification requires letting the system run for hours and then assessing a complex outcome, very expensive. Limited improvement.
The mechanism is not subtle. Modern post-training is dominated by methods that generate candidates and select among them using a signal. Where the signal is cheap and accurate, you can generate an enormous amount of it and the training loop compounds. Where the signal requires human judgement or elapsed real-world time, the loop is throttled by the cost of the signal.
Capability is not distributed by difficulty. It is distributed by how cheaply you can tell whether you got it right.
The useful corollary is predictive. If you want to know where capability will improve next, look for domains where verification is about to get cheaper — through better simulators, through formalisation, through instrumented environments — rather than domains that seem intellectually adjacent to ones that have already improved.