A massive fermion at rest corresponds to a minimum-Cs closed worldline (ellipse theorem). Its internal oscillation frequency is ωrest = M (Compton relation in Planck units). The spectral complexity of this worldline is
with Δω = ℏ ln2. The dominant frequency term gives
Thus E = mc2 is the statement that the informational cost of encoding persistent matter equals its rest energy. Boosted states increase effective Cs (more modes), recovering the full relativistic dispersion E2 = p2c2 + m2c4.
Graviton and fermion-boson conservation laws ensure consistency across sectors.