Uniform Stability of the Spherical Laughlin Gap
We prove that the fermionic Laughlin V 1 Hamiltonian at filling 1/3 on expanding round spheres retains a unique ground state and a uniform spectral gap under sufficiently weak bounded real scalar one-body potentials projected to the lowest Landau level. With coefficient one for each pair projector and Laughlin flux $q=3(N-1)$, the gap and perturbation threshold are uniform for all sufficiently large particle numbers and all potential profiles of supremum norm at most one. The result uses the uniform unperturbed Fock-space gap and gives existential constants.
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