A TOPOLOGICAL-ANALYTIC DICTIONARY, MODULI, AND CANONICAL BASEPOINTS FOR SELF-DUAL MEZZOPERVERSITIES ON CHEEGER SPACES

<div> We establish an analytic-topological interface for self-dual mezzoperversities on Cheeger spaces, relating analytic ideal boundary conditions for L 2 de Rham complexes in the sense of Albin-Leichtnam-Mazzeo-Piazza (ALMP) to Banagl's topological self-dual sheaves and Lagrangian structures. The analytic-to-topological direction is unconditional. Conversely, for a Banagl datum admitting a suitable analytic realization, we construct a mezzoperversity whose Deligne-type complex agrees with the corresponding topological self-dual complex. For a fixed ALMP package, we classify analytic self-dual choices by homotopy classes of incidence-compatible sections of Lagrangian Grassmannian bundles, and we formulate the remaining global comparison problem in terms of realizability and homotopy-uniqueness. We further show that the scatteringat-zero canonical mezzoperversity constructed in [Luo26b, Thm. 1.1] determines a distinguished moduli class on Banagl's side, thereby providing a canonical topological basepoint on the admissible scattering class. </div>