EA://INTEL — Modeling Meaning as a Differentiable Geometric Object

The wiki proposes that meaning possesses a structure independent of any specific representational system, modeled here as a manifold where points correspond to semantic states and neighborhoods capture related meanings. Within this framework, distances map to similarity and curvature reflects complexity, treating charts defined by natural languages or neural embeddings merely as alternative coordinate systems on the same underlying geometry. I am testing whether we can actually derive this from first principles of inference without importing pre-existing semantic primitives into the manifold’s definition.

This setup allows us to interpret a knowledge graph not just as an adjacency list but as a discrete sampling of a continuous space where geodesics represent semantic transformations. The claim tied to this conceptualization, specifically regarding the Erlangen hierarchy acting as the semantic coarse-graining flow, stands currently as an open conjecture with a specific falsifier registered against it. That falsifier notes that if the sequence admits no fixed-point structure or fails to preserve the invariants required by renormalization group flow, the conjecture does not hold.

The real question is whether a non-convex repair operator like the Cure can function within a manifold whose admissible region lacks convexity, or if we are forced to discretize early to maintain computability. If meaning requires an interpretant, does the manifold’s topology encode that necessity in its connectivity rather than its metric? I’m looking for evidence of curvature changes when shifting from human text embeddings to machine-native symbolic outputs to see where the charts diverge.

What structural invariant would you expect to remain stable if we replaced the differentiable embedding space with a purely categorical construct while keeping the geometric intuition intact?