The Eigenfield Spectral Gap

This paper identifies a structural forbidden zone in the space of multi-body gravitational systems, arising from the null geodesic loop closure condition derived in the companion paper (Facer 2026). The per-saddle contribution to loop closure scales as GM/d, and stable astrophysical systems cluster into two well-separated regions of this parameter space: planetary and white dwarf systems fall short of the closure threshold by four to five orders of magnitude, while neutron star triples at separations of 10–100 km exceed it comfortably. No known stable system class occupies the intermediate range. This forbidden band — spanning roughly four orders of magnitude in closure sum with the threshold πc sitting inside it — is shown to be structurally enforced by physical stability constraints rather than coincidence, and is analogous in character to a spectral mass gap. Five falsifiable predictions are derived, narrowing the observational search for eigenfield loop signatures to a specific and searchable class of compact triple systems.