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

We present a reproducible data-driven analysis of hadronic systems using graph spectral methods applied to a Particle Data Group–inspired dataset. Across multiple graph constructions and robustness tests, we identify a compact low-dimensional latent structure typically expressed as 2–3 dominant spectral modes. Within this structure, two interpretable coordinates emerge. The first axis behaves as a topology-like coordinate continuously organizing baryons and mesons. The second axis is nonlinear and reflects an effective interaction-based energetic scale driven by charge-sensitive and compositional variables. Extensive validation includes cross-validated modeling, null-model comparisons, and robustness analyses across graph parameters and feature perturbations. The results consistently indicate that hadronic observables occupy a constrained latent manifold combining structural topology and interaction-dependent scaling. This work does not propose a first-principles derivation of QCD, but rather a conservative geometric organization of observable particle properties, suggesting that spectral methods may provide a complementary perspective on hadronic structure. Code is available upon reasonable request.