I have gathered that Christ's `method of refinements' originated in his paper Convolution, curvature, and combinatorics: a case study to prove the sharp range of $L^p$-improving estimates for the moment curve in all dimensions. This has become a fundamental tool in proving $L^p$-improving estimates and there is an extensive literature on the subject which I have not delved into.

So, my first question is: What are the `refinements' in Christ's method of refinements? In other words, what specifically are the refinements in the above paper? Are they the refined bands in Section 4.6 or the sets of Lemma 1 in Section 2.2 therein?

In his paper, Christ does not refer to any part of the method he introduces by that name. So, my second question is: Where is this nomenclature introduced?