A Spatial Branching Hypothesis for Matter and Antimatter within the Graviton-Connectivity Framework

This work extends the graviton-connectivity framework previously proposed for emergent spatial geometry by introducing a new hypothesis concerning the spatial relationship between matter and antimatter. In the preceding framework, paired excitations and nonnegative relational links are represented by a weighted graph, and spatial dimensionality is evaluated using graph-theoretic quantities such as the graph Laplacian, spectral dimension, and volume-growth dimension. That formulation does not itself imply a separation into matter- and antimatter-dominated universes. Here, we investigate a possible extension in which matter-associated and antimatter-associated excitations form two relational sectors within an enlarged connectivity structure. The total weighted connectivity matrix is represented in block form, with intra-sector connections for the matter and antimatter sectors and cross-sector connections between them. A dimensionless branching parameter is introduced as the ratio of cross-sector connectivity to intra-sector connectivity. When cross-sector connectivity becomes strongly suppressed while each sector independently develops a stable approximately three-dimensional spectral regime, the resulting structure may be interpreted as two emergent spatial branches rather than two distant regions embedded within a pre-existing common space. This proposal is speculative. It does not establish that the physical Universe contains a separate antimatter universe, nor does it derive the required branching dynamics from the existing graviton-connectivity action. Instead, it provides a mathematically testable extension of the framework and identifies specific conditions that would have to be demonstrated numerically or analytically. The model also distinguishes cosmological relational branching from laboratory antimatter production. Locally produced antiparticles are not assumed to leave ordinary spacetime or possess negative gravitational mass. The hypothesis therefore defines a possible research direction for studying whether matter–antimatter symmetry could be expressed not only through particle properties but also through the emergent relational organization of space.