Algorithmizing the entropic proof of the PFR conjecture
Determine whether the entropic methods employed in the combinatorial proof of the Polynomial Freiman–Ruzsa (PFR) conjecture can be transformed into efficient, explicit algorithms that construct the covering subspace, thereby yielding an algorithmic proof aligned with the original entropic approach rather than relying on alternative quantum or dequantization techniques.
References
Unfortunately, the aforementioned proof heavily relies on entropic methods that are non-algorithmic by nature and it is unclear whether such machinery can be transformed into efficient algorithms.
— Algorithmic Polynomial Freiman-Ruzsa Theorems
(Arunachalam et al., 2 Sep 2025) in Introduction, Technical overview