Meaning
The orbit floor is the lowest value a height function approaches anywhere along a symmetry orbit.
For a group G acting on X and a nonnegative height h, define ρ_G(x)=inf_g h(gx). Moving x along the same orbit leaves the set of tested values unchanged, so the floor is invariant. GAT V then forms the operator Q_G=∫ρ_G(x)² dE(x) using the covariant spectral measure.
Example (illustrative)
If a finite orbit has heights 2, 5, and 7, its floor is 2 at every point of that orbit. For an infinite orbit the infimum need not be attained: heights can approach zero while remaining positive at every individual point.
Scope and limits
A positive height in one frame or at one point is not a positive orbit floor. Interpreting Q_G as invariant mass requires the source’s physical spectral-identification hypotheses.
Source
GAT V — Invariant Spectral Transfer. GAT V, Definition 3.2.