Curvature in the Honeyverse

Paper 3 of an 8 part series. This paper develops a dual‑geometric description of curvature within the Honeyverse framework. The primal Honeycomb Unit (HU) lattice encodes local curvature through deficit angles associated with its tetrahedral–octahedral structure, providing a discrete analogue of metric curvature. The ghost dual complex encodes global curvature through its combinatorial expansion, forming adjacency shells whose growth rate defines a large‑scale curvature hierarchy. By analyzing the relationship between these two structures, the paper shows how the Honeyverse naturally separates curvature into local metric contributions and global combinatorial contributions. This dual‑curvature picture becomes essential for understanding holography, information flow, and the emergence of cosmological scales in subsequent papers. v1