My guess (or at least my hope) is that you and I are coming at the same problem from two different angles. Like a theory of physics, where one person (me) starts with simple observations / physical assumptions, the other person (you) builds some abstract mathematical tools; at first these seem like totally unrelated ideas, and only later do they discover that the mathematical tools are needed to use (or even to state) the theory to its fullest extent. I still haven’t connected the dots. What do elliptic curves have to do with class threads? Should we expect a class thread to be points on an EC through embedding space? Or something like that?

I think you’re right — we are approaching the same terrain from different directions. But the elliptic curve is not the ontology. It’s not that class threads are points on an EC in embedding space. That framing drifts back toward “geometry of meaning.” That’s not what I’m doing. Class threads are structural constraints in the knowledge graph: minimal canonical node types minimal canonical relation types vertical and horizontal weaving compositional consistency That’s ontology discipline. Elliptic curves enter at a different layer. They are a state space substrate. Think of it this way: Tapestry / class thread principle defines: → what structures are allowed. Elliptic traversal defines: → how state transitions occur inside a closed algebra. So it’s not: “Each class thread is a curve.” It’s more like: “The algebraic state transitions that represent class-thread-consistent extensions live inside a closed group.” The EC provides: finite cyclic structure closure under composition inverses bounded growth deterministic traversal It’s a motion engine, not a semantic embedding. You could implement class threads without elliptic curves. But if you want: compositional determinism bounded, non-exploding traversal cryptographically anchorable state commitments algebraic auditability then a compact algebraic group is attractive. So the connection is not geometric embedding. It’s this: Class threads minimize ontology complexity. Elliptic algebra minimizes transition complexity. One governs structure. The other governs motion. If they converge, it won’t be because threads are points on curves. It will be because: Minimal ontology + minimal algebra = stable, composable knowledge growth. That’s where the two approaches may meet. Not in embedding space. In constraint space.