class threads sounds like category theory, class and category are very adjacent to each other as concepts. the elliptic curves are a coordinate space that is populated by using hashes of the data, using deterministic, lossless compression algorithms, to eliminate redundancy and highlight the distinctions, which then can become new facts, populate new types, categories and grammars. elliptic curves are most well known for the discrete log probllem, which makes reversing a traversal able to conceal the path backwards, enabling ECDH and pubkey derivation, to the point where it's practically impossible to crack them, without using side channels, or otherwise breaching the actual location where the secret is stored, which could be impossible in the case of a fanatical or determined attacker being interrogated. i'm not sure so much that topology is involved, except in as far as adjacent concepts are closer together by hamming distance with the right proximity hash being used, it's more of a coding theory thing, i think.

I’m thinking the class thread rule for LLMs could be something like the Einstein equation for 4-manifolds. In both cases, we have a continuous space, the shape of which is constrained by an equation. An untrained LLM doesn’t follow the class thread rule, but a well trained one does. So tapestry theory would have several uses: 1. How to read the graphical (compressed) representation of the embedding space directly 2. How to detect when training is incomplete: measure the extent to which the class thread rule is or is not fulfilled. 3. Corollary to 2: how to guide LLM training to those areas where the class thread rule is being poorly followed.