If you look through Ryan Williams' x thread he links to a google drive folder (https://drive.google.com/drive/folders/1SAqEO1kt6wnA0NXuZecy...) with the OpenAI and Anthropic papers. There is also a new human contribution which is pretty accessible from Amit Sahai. I found this paper to be a more reasonable read, although the author(s) do state that their goal is to demonstrate a subexponential bound via an easier to follow approach.

Maybe it's a bit early to predict here but it feels like this approach might have a series of improvements similar to the progress made on the faster FFT multiplcation result.