I switched my search for low kurtosis directions in spectrum space into a search for bimodal directions. That is, I wrote down a scalar (which has to do with k-means with k=2) that decreases as a distribution becomes more bimodal. Then I searched Tsalmantza's high-variance PCA components for directions in the space that are
most bimodal. I find three, perpendicular bimodal directions! Of course each one is a different version of the red–blue galaxy bimodality, of which I have been an unheard critic. More on this as I understand it better.
Surhud More (MPIA) and I began working this week on the monopole term in the opacity of the Universe, using the consistency of baryon-acoustic and supernovae measures of the expansion history to check the phase-space conservation of photons. This test is (nearly) independent of world model, as it depends almost entirely on purely special-relativistic considerations. We hope to have an LPU (least publishable unit) on the subject soon.