Latent Low-Dimensional Spectral Structure of Hadronic Systems via Graph Laplacian Embedding

This work presents a data-driven graph-spectral analysis of a PDG-inspired dataset of 206 hadrons, including both baryons and mesons. Using Laplacian embedding, the study reveals a robust low-dimensional latent structure characterized by two dominant spectral coordinates. The first coordinate behaves as a topology-like axis associated with baryon-versus-meson organization, while the second corresponds to a nonlinear energetic coordinate. Nonlinear models (gradient boosting and random forest) achieve strong generalization performance (cross-validated R² ≈ 0.97), with shuffle controls collapsing to negative values, supporting the presence of a structured latent signal. Feature-importance analysis indicates that interaction-based variables, particularly charge and mass × charge, dominate the second coordinate, while normalized descriptors such as mass per quark remain informative but secondary. This work provides a reproducible and conservative data-driven perspective on the geometric organization of hadronic systems, without claiming a derivation from first-principles QCD. Implementation details and computational pipeline are intentionally withheld in this initial release and will be disclosed in subsequent work.