A Two-Cluster Structure in the Standard Model Fermion Mass Spectrum: A Data-Driven Clustering Analysis

We introduce a latent mass-participation parameter and examine the distribution of the 12 Standard Model fermion masses under monotonic embeddings. The analysis reveals a two-cluster structure: neutrinos at d_μ ≈ 0. 00–0. 12 and massive fermions at d_μ ≈ 0. 60–0. 99, separated by a statistically nontrivial gap (p = 0. 012 under a log-uniform null, Monte Carlo N = 100, 000). The gap is robust across exponential, power-law, and quadratic embeddings, survives ±10% mass perturbation (bootstrap 95% CI: 0. 48, 0. 50), and shows strong clustering (silhouette score 0. 81). Extension to massive gauge bosons (W, Z, Higgs) improves significance to p = 0. 002 (N = 15 particles). The gap corresponds to a 7-order-of-magnitude mass desert (~0. 05 eV to ~0. 5 MeV) containing no known fundamental particle. We present three testable expectations, including consistency with normal neutrino mass ordering.