New lower and upper bounds have been established for the Grothendieck constant $K_G$, specifically $\frac{6\pi}{11}\le K_G\le\frac{\pi}{2\log(1+\sqrt2)} - 10^{-4}$. The lower bound was derived by identifying limitations in asymptotically optimal Krivine schemes, a departure from prior methods that focused on explicit constructions.

For the upper bound, the researchers introduced and analyzed the first asymptotic construction of rounding schemes. This contrasts with earlier work that concentrated on low-dimensional schemes. These refined bounds have precisely determined the previously unknown tenths digit of $K_G$ to be 7.

The discovery of these bounds was the result of a sustained, collaborative effort involving both human researchers and a long-horizon AI research system developed by the team. The work was submitted by Rahul Saha.