### 4.3 Real cuts from the complex good cuts, II

The construction of real structures from the complex structures, i.e., finding the complex
values of that yield real values of and the associated real cuts, is virtually identical to
the flat-space construction of Section 3. The only difference is that we start with the GCF
rather than the flat-space
Using , Equation (200) is written

Update The reality of , i.e.,
again leads to
and the real slicing,
Using Equation (191) and expanding to first order in , we have the expressions:

Since in all applications is multiplied by a first-order quantity, only the first-order expression for
is needed. Using the slow motion assumption, we have,
Substituting this into Equation (206), via the slow motion assumption, leads to the real cut function
:
Later the linear versions are extensively used: