ProbXiv
sign in
Problem archiveProblem record

The Matrix Spencer Conjecture for Finite Groups

Probability & statistics · posed by Nikhil Bansal, Haotian Jiang, Raghu Meka, 2022 · solved

1 comment

Statement

The group version of the Matrix Spencer conjecture holds: for every finite group GG there are signs ε∈{±1}G\varepsilon \in \{\pm 1\}^G with ∥∑g∈Gεgρ(g)∥≤C∣G∣\left\|\sum_{g \in G} \varepsilon_g \rho(g)\right\| \le C\sqrt{|G|}, where ρ\rho is the left regular representation and CC is universal.

Record

Source
Added
Links

Comments

No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Afonso S. Bandeira and Helmut Bolcskei, using ChatGPT Pro 5.5, Claude Opus 4.7 and 4.8

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The acknowledgement says modern AI tools were used throughout, and singles out one of the key arguments as the one that broke the problem open, crediting it to that use.

    the group case; the full Matrix Spencer conjecture remains open

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.