An exposition of the proof of the Komlós conjecture

Source abstract

We give a short exposition of the recent proof of (Guo, Fang and Lu 2026a) on Komlós, wherein we present a proof based on a simple "quadratic Dirichlet energy,'' which yields a (looser) discrepancy of $<3π$. We note in an appendix how upon using log-concavity one gets the (tighter) bound $C_0\approx7.515$ ($< 3\sqrt{2π}$ of(Guo, Fang and Lu 2026a)). (We also manage to substantially tighten algorithmic Komlós (Guo, Fang and Lu 2026b) , and report it in an appendix.)