Motivic Resurgence of Anomalous Wall-Crossing Invariants: Non-Perturbative Mapping of Flux-Deformed Calabi-Yau Derived Categories

Mathematical Applications of Science Fiction We present a rigorous construction of the non-perturbative completion of the motivic Hall algebraassociated with a flux-deformed Calabi-Yau threefold Xℏ. By analyzing the anomalous wall-crossingbehavior of Donaldson-Thomas invariants under the influence of a non-trivial H-flux background,we demonstrate that the generating series of these invariants exhibit resurgent behavior in the Borelplane. We define a canonical isomorphism between the filtered derived category of coherent sheaves onthe deformed variety and the algebra of resurgent transseries. Central to this work is the derivationof a Modified Kontsevich-Soibelman wall-crossing formula that accounts for holomorphic anomaliesvia alien calculus. We prove that the Stokes automorphisms across singular rays in the Borel planecorrespond precisely to the mutation of the exceptional collection in the derived category. Thisframework provides a complete resolution to the divergence of the perturbative topological stringpartition function, suggesting a stable vacuum structure in the underlying multiverse cosmology.