ZKPs verify "things" by encoding the verification in a computation, and verifying that the computation happened in the right way, means to assess it was computed correctly, i.e., with the right inputs, the right operations, etc. So this is what I meant with "correctness".

The bottleneck has two sides: first, there's a technical bottleneck. ZKPs are quite expensive, and finding the right, production-ready protocol is challenging. The other side is a socio-technical bottleneck. There is always quite a large friction with adopting these kind of technologies, also due to the first bottleneck.

As you said, it is difficult to adopt because of how fast the complexity grows with big models. It's great indeed to see that Anthropic is tackling the challenge.