Can there be an explicit expression of g as defined in the link?

This is related to the article in the link: https: //arxiv.org/pdf/1610.08468.pdf titled Algebraic normalization of regularity structures. In the functionalization re-normalization method. $ g $ shown on page 6 plays an important role. However, in the document there is no explicit expression of $ g $ shown (as an example for a particular pde). Is there a reference where I can finance such an example? Any comments or suggestions?