Optimal Vector Balancing for Zonotopes

For every zonotope $Z \subset \mathbb{R}^d$ and vectors $v_1,\ldots,v_n \in Z$, there are signs with $\sum_i x_i v_i \in C\sqrt{d}\,Z$ for a universal constant $C$. This resolves a 2002 conjecture on vector balancing in zonotopes.

Result

Proved

Status

Resolved

AI contribution

AI-assisted

Method

Argument

Field

Discrepancy theory

Posed by

vector balancing literature

Year posed

2002

Years open

24y

Solved

2026-05-22

Model

GPT-5.5 Pro

Vendor

OpenAI

Collaborators

Victor Reis

Verification

Unreviewed

Publication

Preprint

Significance

20 / 100*

Disclosed cost

—

Wikipedia

No dedicated article