The "refinement" terminology in connection with Christ's <A HREF="https://math.berkeley.edu/~mchrist/Papers/kielslides.pdf">1998 paper</A> seems to originate from Tao and Wright's <a href="https://arxiv.org/abs/math/0108137">2001 article</a>, although the earliest explicit reference to "Christ's method of refinements" I could locate is a <A HREF="https://www.semanticscholar.org/paper/A-non-linear-generalisation-of-the-Loomis-Whitney-Bennett-Carbery/fc2039a582e16fb3d5364057af8e58827655e55d">2005 article.</A> Christ himself speaks of a "refined band structure".