Submit progress

on Marton's conjecture constant (PFR) ($C_{18}$)

The statement

$C_{18}$ is the least constant such that, whenever $A$ is a subset of $\mathbb F_2^n$ with $\lvert A+A\rvert \leq K\lvert A\rvert$ , then $A$ can be covered by $K^{C_{18}+o(1)}$ cosets of a subspace of cardinality at most $\lvert A\rvert$ , where the limit $o(1)$ is with respect to the limit $K \to \infty$ .

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.