KAM Stability of Quasi-Periodic Orbits in Multi-Body Exoplanetary Resonance: A Motivic Approach via Derived Symplectic Geometry

Mathematical Applications of Science Fiction We present a rigorous derivation of the persistence of quasi-periodic invariant tori in Hamiltonian systems governingN -body exoplanetary architectures near mean-motion reso-nances. Departing from classical perturbative techniques, weemploy a Nash-Moser iterative scheme formulated within thecategory of derived symplectic stacks. We define a MotivicDiophantine Condition on the frequency vector ω ∈ Rn, uti-lizing the zeros of automorphic L-functions to bound smalldivisors. We prove that for perturbations ε bounded bythe Gevrey class of the Hamiltonian, the set of survivingtori forms a Cantor set of positive Hilbert-Schmidt measure.The proof necessitates the construction of a renormalizedhomological operator acting on the étale cohomology of thephase space. We further demonstrate that the diffusion ofactions (Arnold diffusion) is topologically obstructed by thenon-triviality of the Chern-Simons invariants of the resonantmanifold.