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This is the first paper in a series which proposes and develops the polyfoldFredholm structure--Kuranishi structure correspondence, identifying these twoabstract perturbative structures which are indispensable for constructing andunderstanding symplectic invariants in the most general settings. In thispaper, I present my version of the theory of Kuranishi structures in fullgenerality. This theory is independent of all the choices made in theconstruction (including the choices of good coordinate systems); and it usesthe equivalence of Kuranishi structures as the germ to capture the intrinsicunderlying structure to which the perturbation theory descends. This is thefirst theory in the literature that has these two properties. Thischoice-independent theory is essential for canonically and functoriallyidentifying the polyfold Fredholm theory of Hofer-Wysocki-Zehnder with thetheory of Kuranishi structures. The next two papers in this series will be onthe forgetful functor and the globalization functor in the respectivedirections of the polyfold--Kuranishi correspondence, as well as illustratingthe use of the correspondence with a few sample applications.

The polyfold--Kuranishi correspondence I: A choice-independent theory of Kuranishi structures