This actually sounds really interesting. As a game, it lets you explore the geometry of an LLM and how it associates things. I'd be curious how this is getting

This actually sounds really interesting. As a game, it lets you explore the geometry of an LLM and how it associates things. I'd be curious how this is getting formatted into prompts. Also curious if there's any other properties these relationships exhibit. I'm guessing there is no zero element, where "x + 0 = x" for all x. I'm also guessing there's no idempotent elements, where "x + x = x". There's probably no ability to loop around in general. But I'm curious if this is cancellative, i.e. if x + y = x + z imply y = z. I'd also be curious to see if there's any sort of embedding or approximation from this structure into another. At first I thought of word2vec embeddings, and how addition of vectors could have some logical structure. But that algebra is associative. Maybe mapping it to some algebra where x * y = f(x + y), where * is the non-associative operation, x+y is vector addition of the embeddings, and f is some transformation. Actually, that could be interesting. If you could find some embedding and f transformation that very closely matched the Infinite Craft algebra, you could use the difference between x and f(x) as vectors to try and quantify the degree to which the algebra fails to be associative.