  We explain how to adapt the methods of Abouzaid-McLean-Smith to the setting
of Hamiltonian Floer theory. We develop a language around equivariant
``$\langle k \rangle$-manifolds'', which are a type of manifold-with-corners
that suffices to capture the combinatorics of Floer-theoretic constructions. We
describe some geometry which allows us to straightforwardly adapt Lashofs's
stable equivariant smoothing theory and Bau-Xu's theory of FOP-perturbations to
$\langle k \rangle$-manifolds. This allows us to compatibly smooth global
Kuranishi charts on all Hamiltonian Floer trajectories at once, in order to
extract a Floer complex and prove the Arnol'd conjecture over the integers. We
also make first steps towards a further development of the theory, outlining
the analog of bifurcation analysis in this setting, which can give short
independence proofs of the independence of Floer-theoretic invariants of all
choices involved in their construction.
