Research proof index

If $A \subset {\bf F}_2^n$ is finite non-empty with $|A+A| \leq K|A|$, then there exists a subgroup $H$ of ${\bf F}_2^n$ with $|H| \leq |A|$ such that $A$ can be covered by at most $2K^9$ translates of $H$.

Polynomial Freiman-Ruzsa theorem with exponent $9$, without a finite ambient-group assumption. Let $A$ be a nonempty finite subset of an elementary abelian $2$-group. If $|A+A|\le K|A|$, then there are a finite subspace $H$ and a finite set $c$ such that $A\subseteq c+H$, $|c|<2K^9$, and $|H|\le|A|$.

RBR knowledge soundness for a single round oracle verifier

Perfect completeness for the core interaction oracle reduction

Round-by-round knowledge soundness for the core interaction oracle verifier

Round-by-round knowledge soundness for the final sumcheck step