A Mode Budget for the Lamb Shift: How Much of the Shift Each Decade of Vacuum Fluctuations Supplies

The Lamb shift, the 1057.8 megahertz splitting between the 2S and 2P levels of hydrogen, is the textbook proof that vacuum fluctuations do physical work inside atoms. This paper apportions that work across energies. In a logarithmic budget running from the atomic scale of 13.6 electronvolts to the electron rest energy, one percent of the shift has accumulated only by 15.1 electronvolts and half only by 2.636e+03 electronvolts. The characteristic scale of the vacuum density that survives gravitational accounting, 2.240 milli-electronvolts as derived in the accompanying script, falls below the bottom of the budget entirely. The conclusion is plain: the Lamb shift certifies vacuum fluctuations across electronvolt-to-kiloelectronvolt energies, and it is silent about the milli-electronvolt remainder that gravitation appears to register. The apportionment is computed from a stated logarithmic model, not measured.