Planck Mass as a Product of Six Standard Model Particle Masses: An Empirical Observation

We report an empirical numerical relation connecting the Planck mass to a product of six Standard Model particle masses: mμ · md · mW · mZ · mH · mn = mPl · me⁵. Using PDG 2024 central values, this holds to 0.05% accuracy (0.005σ). An exhaustive combinatorial search over all 8,191 subsets of 13 particle masses identifies this six-particle set as uniquely accurate — the closest match among 1,716 possible six-element subsets by a factor of ~11. The set {μ, d, W, Z, H, n} constitutes a minimal complete basis of the Standard Model, covering all six independent mass-generating sectors. The coincidence of numerical precision with structural completeness yields an estimated significance of ~2.5–3.0σ after accounting for look-elsewhere effects. The relation yields a testable prediction: md = 4.668 ± 0.006 MeV, falsifiable by future lattice QCD calculations. No theoretical derivation is offered or claimed.