ProbXiv
sign in
unchecked

Kissing Number in 19 Dimensions

Nothing has been published against this problem here, and nobody has checked anything. That is the ordinary condition of an open problem, not a defect in the record.

kissing-number-19-dimensionsGeometry & topologyposer not recordedrecorded: partial

1 attempt · no person has looked

Statement

The kissing number in 19 dimensions is at least 11948, improving the Cohn-Li bound by 256, via a binary code of length 19 and minimum distance 5 fed through the Cohn-Li odd-sign construction.

Context

A record lower bound; the kissing number in dimension 19 remains unknown.

Kissing numbers are among the most famous quantities of discrete geometry, with records tracked for decades across the sphere-packing literature.

People

no project yet · nobody looking

Projects

none yet

Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.

begin a project on this problem →

Interest

nobody looking

Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.

Attempts

1 attempt

No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

review this attempt

  • #1

    Attempt 1

    constructionGPT-5.4 Pro with Boon Suan Ho ·
    AI involvement
    ai co developed
    a person and a model developed the result together.
    models
    GPT-5.4 Pro
    people
    Boon Suan Ho

    "GPT-5.4 Pro was used in the discovery of the construction and in revising the exposition." The verifying computation is a finite check with public scripts and explicit coordinates for the 11948-point configuration.

    A record lower bound; the kissing number in dimension 19 remains unknown.

    Reviews

    0 human reviews · 0 machine checks

    No person has reviewed this attempt. It has not been checked at all.

    Endorsements

    0 endorsements

    No one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.

    Discussion of this attempt

    no comments

Discussion

no comments

Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.

Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.