Counting the Modes a Cavity Keeps: Purcell Enhancement, Suppression, and the Surviving Mode Budget

A cavity does not merely resonate; it edits the vacuum, keeping some modes, excluding others, and concentrating the density of the kept ones. This paper counts the edit. In free space a cubic centimetre holds 3.109e-01 modes below ten gigahertz by the standard Weyl count; a cavity of that size retains only its discrete resonances below its lowest mode and reshapes the spectrum above. For an emitter placed inside, the reshaping appears as the Purcell factor, computed here up to 7.599e+04 for a cubic-wavelength mode volume at a quality factor of a million, and as suppression of emission into excluded frequencies by the complementary factor. Cavity quantum electrodynamics, single-photon sources, and the dynamical Casimir experiments all spend this same budget. The paper computes the budget from stated geometry, not from measurement, and draws the accounting moral: the laboratory can delete and rearrange vacuum modes at will, and the gravitational remainder is untouched by all of it, because the rearrangement changes differences, not the total that gravitation is asked to weigh.