Every iterated paraproduct has local Taylor-type expansions described by one universal regularity structure, and every paracontrolled system lifts to a modelled distribution on that structure.
and Hoshino M., Paracontrolled calculus and regularity structures II
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Local expansion properties of paracontrolled systems
Every iterated paraproduct has local Taylor-type expansions described by one universal regularity structure, and every paracontrolled system lifts to a modelled distribution on that structure.