In the development of this paper I worked for while with Astra to find a proof of the "improved light patterns lemma" (Lemma 10). Eventually it spit out the proof below; I spent some time trying to understand it and reorganize the argument, but ultimately abandoned this for the much simpler argument in the above linked paper (that argument was also found by Astra). This abandoned argument involved a kind of reverse-hypercontractive inequality which perhaps could be of some use to someone somewhere, so I'm posting it here. The brief writeup includes the application to "light patterns." The writeup is entirely by Astra, I got some of the way through "deslopification" before abandoning this argument so if anyone finds a use for this they'll have to do the rest of the deslopifying themselves.