theory as detailed in [@FOOOCF]. We note that a good coordinate system constructed directly from a Kuranishi structure defined in [@FOOO] without extra conditions will a priori have orbifold sections in Kuranishi charts and orbibundle embeddings as coordinate changes. Thus, in [@FOOONEWER], [@FOOOCF], Kuranishi charts and coordinate changes in a Kuranishi structure are respectively formulated as (not necessarily global quotient) orbifold sections and orbibundle embeddings, so that charts and coordinate changes of a good coordinate system obtained are of the same form/category as those of the starting Kuranishi structure (as one might need to go back and forth, at least partially, between these two different types of structures), and abstract perturbation theory works as well. However, the version of [@FOOO], [@Dingyu], [@DI] are written with global quotient charts and coordinate changes. So on one hand, they can adapted to the general orbifold versions without much conceptual difficulty (see discussion in [@DI] 1.3 (4) about local models); on the other hand, it would still be nice to work harder as in [@MAXCAT] and achieve global quotient charts and coordinate changes in the associated good coordinate system directly without rewriting or re-interpretation of prior works. And the relationship of such a good 