thesis [@Dingyu] is about the abstract correspondence between polyfold theory and theory of Kuranishi structures, as well as a theory of Kuranishi structure R-equivalence classes via level-1 structure. This work was inspired from a vision of Helmut Hofer, that is, one should be able to construct a polyfold analogue [@Yang] of Joyce’s innovative Kuranishi Homology (KH) [@KH]. The point of KH is that no perturbation is needed. For a simple example, a certain equivalence class of a map (added with some gauge-fixing/stability data to ensure finite automorphisms) from a Kuranishi structure without boundary to an orbifold will immediately give a cycle in Kuranishi homology theory of this orbifold without any perturbation. The perturbation is in some sense pushed to the proof of showing KH is isomorphic to rational singular homology, so it is like a non-perturbative homology theory (or universal perturbation theory). Since the polyfold constructions of moduli spaces are canonical as we shall briefly indicate below, polyfolds are global (with two-way coordinate changes) and sc-Fredholm theory formally looks like a Sard-Smale theory, the construction will be simpler, and after developing some properties of this non-perturbative homology theory, one can get invariants without ever worrying about transversality. I have a 