Cosmological Constant from Spectral Residuals in the Floriano Unified Theory

Within the Floriano Unified Theory (TUF), we derive the observed cosmological constant Λ_obs from first principles using zero free parameters. The derivation has two parts: (1) exact cancellation — the electron, as the unique zero mode of the hyperspace Dirac operator D_Ξ, forces the vacuum curvature R(Ξ)|_vac = 0 via the Atiyah–Singer index theorem, cancelling the vacuum energy identically; (2) residual Λ from spectral resonance — three resonances between PSL(2,p) representation theory and TUF quantum numbers determine the moduli-space volume Vol(Ξ)/ℓ_P⁴ = 7×19×409 = 54397, yielding Λ_TUF = 1.108×10⁻⁵² m⁻², agreeing with Λ_obs = 1.106×10⁻⁵² m⁻² to 0.20% with zero free parameters. Open problems explicitly documented: the p=7 and p=19 PSL(2,p) resonances are algebraically sharp for p=409 but remain conjectural for p=7 and p=19, pending rigorous derivation from representation theory. This paper is part of the TUF series:- Paper 0 (Ontological Foundation): https://doi.org/10.5281/zenodo.19024705- Paper 1 (Fermion masses): https://doi.org/10.5281/zenodo.18988060- Paper 2 (Three generations): https://doi.org/10.5281/zenodo.18991190- Paper 3 (Dark matter): https://doi.org/10.5281/zenodo.18991306