Why Particles Have the Masses They Have

This submission shows that the observed particle mass spectrum is not arbitrary.

When masses are expressed as dimensionless logarithmic ratios,

m → ln(m/m_ref),

leptons, mesons, and baryons fall onto nearly equally spaced additive lattices

labeled by internal quantum numbers such as strangeness and charm.

These lattices are naturally explained by simplex geometry,

with quadratic deviations appearing only as subleading corrections.

The Planck scale emerges as a terminal boundary (end-cap) of this structure,

not as a normalization scale.

Within this framework, gravity and dark components arise

as geometric effects of retained correlation,

rather than as separate substances or new particles.

All results are based on existing PDG mass data

and are directly falsifiable.