Stein Kernels and Normal Approximation for Log-Concave Bilinear Forms

Jiang, Lee, and Vempala conjectured that if $X,Y\in\mathbb{R}^n$ are independent isotropic log-concave random vectors, then $W_2(L(\langle X,Y\rangle),N(0,n))$ is bounded by a universal constant. Subject to Theorems 1.2 and 2.5 of arXiv:2607.24164v1, we prove this conjecture and a rectangular biline