GPT 5.5-Pro Solves 2002 Schechtman Problem on Vector Balancing for Zonotopes

I spent a year of my PhD stuck on a 2002 problem of Schechtman. GPT 5.5-Pro helped me finish: vector balancing for zonotopes (shadows of a cube)! For any zonotope Z ⊂ ℝᵈ, v₁,...,vₙ ∈ Z, there are signs x₁,...,xₙ ∈ {-1, 1} with x₁v₁+...+xₙvₙ ∈ O(√d) Z, sharp. [1/4]