Transfinite Etale Cohomology of Infinitesimal Chrono-Discontinuities: Non-Standard Syzygies of Retro-Causal Monads in Saturated Perfectoid Orbifolds

Mathematical Applications of Science Fiction We construct a rigorous framework for the analysis of infinitesimal chrono-discontinuities within the topology of saturated perfectoid orbifolds. By extending the Scholze–Grothendieck étale site to transfinite ordinals, we define the transfinite pro-étale cohomology groups that capture the causal structure of such spaces. We introduce the Retrocausal Monad, an endofunctor on the category of perfectoid spaces, to model nonlinear temporal feedback loops. The main result establishes a spectral sequence relating the nonstandard syzygies of these monads to the obstruction classes of causal paradoxes. We prove that for a sufficiently saturated hyperfield, the second cohomology group vanishes, implying the topological stability of retrocausal trajectories in the limit of infinite recursive depth.