Symplectic Holonomy and Non-Archimedean Spectral Invariants: A Synthetic Differential Formalism in the Internal Logic of Warp Manifold Topoi

Mathematical Applications of Science Fiction We present a rigorous construction of non-Archimedeanspectral invariants associated with Hamiltonian deforma-tions in the context of Warp Manifolds, formalized withinthe internal logic of a smooth topos EW . By utilizingSynthetic Differential Geometry (SDG), we define thesymplectic action functional on the path space of a non-Archimedean analytic space in the sense of Berkovich. Weestablish a correspondence between the symplectic holon-omy of the connection on the pre-quantum line bundle andthe valuation spectrum of the Novikov ring over a p-adicfield. The main result demonstrates that the spectral ca-pacity of a warp bubble is invariant under Hamiltonianisotopies that preserve the motivic filtration of the Fukaya-Seidel category. We further derive a convergence criterionfor the Arnold conjecture in this setting, utilizing the spec-tral sequence associated with the filtered Tate module. Thisformalism provides a geometric quantization framework forspacetime metrics exhibiting closed timelike curves at themicroscopic scale, with implications for stability conditionsin superluminal transport metrics.