Asymptotic Regularization of Topological Transitions in Fluid Lattices via Harmonic Maass Forms and Mock Theta Operators

The mathematical modeling of non-stationary topological transitions within continuous topological lattices is classically limited by the onset of analytic divergences and conformal anomalies. Standard approaches often require the introduction of artificial cut-offs or phenomenological parameters that violate the local symmetry of the system. This work presents a rigorous analytical framework, based on the application of modular operator theory, to map such transitions while preserving differential continuity. Specifically, a global tuning operator is introduced, founded on the asymptotic properties of Ramanujan's Mock Theta functions, integrated with a canonical decomposition into harmonic Maass forms in their respective holomorphic and non-holomorphic components. The topological evolution of the elementary cells, constrained by the degrees of freedom of the icosahedral point symmetry group, is managed through an exponential rotation operator in the complex plane that transforms linear stresses into pure vorticity gradients. It is analytically demonstrated that the synergistic action of these tools eludes the formation of boundary singularities at the asymptotic limit. The exact algebraic compensation of the symmetries imposes a natural and constant constraint of zero entropy on the topological domain, guaranteeing a dissipation-free geometric evolution. The obtained results provide a new formal tool for the dynamics of continuous lattices, suggesting promising isomorphisms for the mathematical analysis of non-Euclidean structures. Furthermore, by mathematically formalizing a purely geometric genesis for equivalent topological mass, this framework offers robust analytical pathways for practical applications ranging from the physics of fundamental elementary states to topological metamaterials and non-periodic crystallographic phases.