The version in the acknowledgements is the one you want:

> An Anthropic employee used an internal research model to investigate open problems in the theory of cryptography. One of them was about cryptographic constructions based on the average-case hardness of Zero-k-Clique [LLV19, AHY25]. Claude was tasked with verifying and improving the constructions, but instead developed this algorithm, first for the average case, then for the worst case. The session used 16M output tokens with no human input.

> Anthropic shared the algorithm with the authors in September 2026 under a confidentiality agreement, offered compensation, and provided access to the public version of Claude.

> A galactic algorithm is an algorithm with record-breaking theoretical (asymptotic) performance, but which is not used due to practical constraints. Typical reasons are that the performance gains only appear for problems that are so large they never occur, or the algorithm's complexity outweighs a relatively small gain in real-world performance. Galactic algorithms were so named by Richard Lipton and Ken Regan, because they will never be used on any data sets on Earth.

https://en.wikipedia.org/wiki/Galactic_algorithm

Yes because now it opens the door for future algorithms to chip away at that exponent where as in the past it may have seemed that an exponent of 2 was the floor.

Nobody thought this was possible.

3sum hard was colloquially considered to be >= n^2

It's an absolutely unbelievable result! (Personally, this is more meaningful to me than Navier Stokes and feels more surprising - not that an agent did it but the result itself is extremely surprising!)