  Work of Hofer--Wysocki--Zehnder has shown that many spaces of
pseudoholomorphic curves that arise when studying symplectic manifolds may be
described as the zero set of a polyfold Fredholm section. This framework has
many analytic advantages. However the methods they develop to extract useful
topological information from it are rather cumbersome. This paper develops a
general construction of a finite dimensional space of multivalued perturbations
of a polyfold Fredholm section such that almost all elements are regularizing.
These perturbation are globally structured and explicitly described, and, in
cases where the moduli space has no formal boundary, permit a transparent
definition of its (rational Cech) fundamental class.
