Research proof index

entropic_PFR_conjecture: For two $G$-valued random variables $X^0_1, X^0_2$, there is some subgroup $H \leq G$ such that $d[X^0_1;U_H] + d[X^0_2;U_H] \le 11 d[X^0_1;X^0_2]$.

In the project's entropic PFR package with parameter $\eta=1/9$, there is a subspace $H$ and a random variable $U$ uniformly distributed on $H$ such that each reference variable is within six times their mutual Ruzsa distance of $U$: $d(X_1,U),d(X_2,U)\le6d(X_1,X_2)$.

If $d[X_1;X_2] > 0$ then there are $G$-valued random variables $X'_1, X'_2$ such that $\tau[X'_1;X'_2] < \tau[X_1;X_2]$. Phrased in the contrapositive form for convenience of proof.