Automated Geometric Data Synthesis and Unified Field Topology Mapping via Tensorized Hypergraph Autocorrelation

**Abstract:** This paper proposes a novel system, GeoSynth-UTM, for automated generation of geometric data sets and subsequent mapping of unified field topologies. Leveraging advances in tensor field theory and hypergraph representation learning, GeoSynth-UTM creates synthetic geometric landscapes that exhibit complex, multi-scale fractal patterns. These landscapes are then analyzed using a newly developed tensorized hypergraph autocorrelation algorithm, which reveals underlying topological relationships, potentially contributing to a deeper understanding of underlying unified field theories. The system's key innovation lies in the ability to programmatically control the geometry and topology of the generated data, allowing for systematic exploration of diverse physical parameter spaces, significantly accelerating the discovery of previously unknown geometric relationships.