Polymath 6.1 Key -

But the actual breakthrough came from (e.g., $\mathbbF_3^n$). A specific “key polynomial” used in the density increment argument was:

For precise algebraic form, consult the (section “Key lemma” or “Key polynomial”) or the final paper: “Density Hales-Jewett and Moser numbers” (2012). polymath 6.1 key

[ \textKey function: f(x) = \text(# of 0's) - \text(# of 1's) \quad \textmod something? ] But the actual breakthrough came from (e