ProbXiv
sign in
machine only

Erdős Problem #106

Everything below was recorded by a tool. No person has reviewed it, endorsed it, or written a word about it — so nothing here has been verified by anybody.

erdos-106Geometry & topologyposed by Paul Erdős, 1932recorded: candidate

1 attempt · 1 machine check · no person has looked

Statement

If f(n)f(n) is the maximum total side length of nn interior-disjoint squares packed in the unit square, is f(k2+1)=kf(k^2 + 1) = k? An exact rational configuration packs 1717 squares with total side length greater than 44, refuting the identity at k=4k = 4.

Context

A numbered Erdos problem that an unusually dense reference trail on erdosproblems.com (9 sources), setting it above the typical entry in the catalog.

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. There is 1 attempt here and 1 machine check recorded against it. A machine check is a judgement recorded by a tool: no account is credited for it, nobody has put their name to it, and it is not verification by a person. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

review this attempt →

  • #1

    Attempt 1

    computationClaude Opus 5 ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    Claude Opus 5

    The public Lean source credits Codex as formal author; The packing was discovered by Claude Opus 5 (Anthropic) against search infrastructure built and run by the submitter, and verified independently in exact rational arithmetic via separating-axis certificates.

    Reviews

    0 human reviews · 1 machine check

    No person has reviewed this attempt. 1 machine check below — a machine check is not human verification.

    • Machine check · not human verification

      machine: correct

      Recorded from Lean ·

      scope Lean formalization of the result

      A 613-line, placeholder-free Lean proof of the counterexample; the erdosproblems.com page had not yet incorporated the result at audit time.

      No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.

    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.