The Matrix Spencer Conjecture for Finite Groups

The group version of the Matrix Spencer conjecture holds: for every finite group $G$ there are signs $\varepsilon \in \{\pm 1\}^G$ with $\left\|\sum_{g \in G} \varepsilon_g \rho(g)\right\| \le C\sqrt{|G|}$, where $\rho$ is the left regular representation and $C$ is universal.

Result

Proved(see note)

Status

Resolved

AI contribution

AI co-developed

Method

Argument

Field

Discrepancy theory

Posed by

Nikhil Bansal, Haotian Jiang, Raghu Meka

Year posed

2022

Years open

4y

Solved

2026-06-10

Model

ChatGPT Pro 5.5, Claude Opus 4.7 and 4.8

Vendor

OpenAI / Anthropic

Collaborators

Afonso S. Bandeira, Helmut Bolcskei

Verification

Unreviewed

Publication

Preprint

Significance

30 / 100*

Disclosed cost

—

Wikipedia

No dedicated article