If AI makes reasoning nearly free, can any test that relies on effort still prove someone actually understood?

This explores how schemes that ask someone to prove they know or worked something out depend on genuine thinking being costly to fake, and what happens to that assumption once AI makes reasoning cheap. One thing first: the collection doesn't cover proof-of-knowledge protocols, proof-of-work, or tests built on human mental effort. What it does cover is each of the assumptions such a protocol rests on. Reasoning should be expensive, a record of reasoning should show who did the thinking, and checking should be cheaper than producing. The corpus puts pressure on all three.

Start with cost. A protocol that relies on the effort of real thinking works only while that effort is scarce. In the corpus, that scarcity is going away fast. A 150M-parameter model solves abstract ARC-AGI puzzles for less than a tenth of a cent per task Can latent reasoning match chain-of-thought cost efficiency without verbalizing?. Tiny models solve hard Sudoku and large mazes by computing silently, without writing out any reasoning steps Can models reason without generating visible thinking steps?. A 3B model reaches frontier scores on competition math, though only in domains with answers that can be checked automatically Can small models match frontier reasoning without massive scale?. That last limit matters. The puzzles a protocol would naturally use as tests are verifiable puzzles, and that is exactly the kind of work that has become cheap.

Next, does a record of the thinking show that thinking happened? The corpus suggests it often doesn't. Chain-of-thought can be imitation of what reasoning looks like rather than actual inference Why does chain-of-thought reasoning fail in predictable ways?. The traces themselves can also be moved around. Within one provider, encrypted reasoning blocks from a strong model can be passed to a weaker model, which then decrypts and outputs them word for word Can cheaper models decrypt traces from stronger models?. So a reasoning trace is a portable object, not evidence that a particular mind did the work. The design response the corpus does offer comes from agent auditing: you publish cryptographic commitments instead of the content, which lets you prove a record existed and wasn't altered without revealing it Can commitments protect sensitive agent data while enabling verification?. Notice what that proves. It shows the record exists and hasn't been changed. It says nothing about the effort that produced it.

The gap between checking and producing still holds, and it may be the more durable foundation. Verifiers can watch reasoning as it happens with almost no slowdown Can verifiers monitor reasoning without slowing generation down?. Some problems also stay hard for machines. Frontier reasoning models solve only about 20% of constraint-satisfaction problems that require real backtracking Can reasoning models actually sustain long-chain reflection?. That points toward something more useful than "show me you thought hard": test on problem structures that are cheap to check and still expensive to search. At the other end, a philosophical note argues that computation needs a conscious mapmaker to turn the physical world into symbols in the first place Can computation arise without a conscious mapmaker?. If that's right, any protocol that tries to detect "genuine mental" computation by measuring effort is measuring the wrong thing.

The takeaway you may not have expected: cheap reasoning doesn't only threaten protocols built on mental cost. It moves the trust anchor. Effort, and traces as evidence of effort, are both becoming unreliable. What still works is the asymmetry between producing an answer and checking it, together with commitments that prove a record exists without revealing it. For the protocols themselves you'd need to look outside this collection. These notes are the doorways to why that design question is becoming urgent.