ProbXiv
sign in
Problem archiveProblem record

Tightness of the Cohn-Elkies Bound in Dimension 36

Geometry & topology · posed by Henry Cohn, Noam Elkies, 2003 · disproved

1 comment

Statement

Can a Cohn-Elkies auxiliary function certify the best known sphere packing in dimension 3636 as optimal? No. An explicit dual-feasible point for the Cohn-Elkies linear program, built from weight-1818 modular forms for Γ0(24)\Gamma_0(24), shows the two-point linear programming bound in dimension 3636 exceeds the density of the Kschischang-Pasupathy packing by a factor of at least 32.9132.91.

Record

Source
Added

Comments

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

  1. construction · #1

    Rifat Jumagulov, using Claude Fable 5, Claude Opus 4.8, Codex (GPT-5.6)

    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 disclosure reports substantial assistance: the Claude models were used for the construction of the certificate itself, for the verification tooling and for drafting, and Codex was used as an independent cross-check of the certificate computations.

    rules out the two-point LP method in this dimension; the optimal packing in dimension 36 remains unknown

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.