Non-Holomorphic Spectral Deformations of Quantum Modular Forms: A Motivic Derivation of Trans-Universal Period Constants via the Arithmetic of Eichler Cohomology

Mathematical Applications of Science Fiction We present a rigorous construction of a non-holomorphic spectral deformation theory for quantum modular forms of fractional weight, extending the classical Eichler–Shimura isomorphism to a trans-universal motivic framework. By introducing a spectral parameter into the period integrals, we define a family of deformation operators acting on the cohomology of the modular group SL(2,Z). We prove that the obstruction to modularity, typically represented by the period polynomial, can be regularized through a spectral zeta function, producing a set of Trans-Universal Period Constants. These constants are shown to correspond to the periods of a mixed Tate motive associated with the deformation space. Furthermore, we establish a duality between the non-holomorphic Eisenstein series and the limiting behavior of these quantum forms at the cusps of the multiverse moduli space. We conclude with ten fundamental lemmas and five theorems detailing the convergence, cohomological stability, and arithmetic structure of these deformations.