ProbXiv
sign in
machine only

Written on the Wall II, Graph Conjecture 322

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.

wowii-graph-conjecture-322Combinatoricsposed by Written on the Wall II (automated conjecturing)recorded: candidate

1 attempt · 1 machine check · no person has looked

Statement

Let GG be a simple connected graph on n≥5n\geq 5 vertices. If the maximum over all vertices vv of ℓ(v)\ell(v) - the independence number of the subgraph induced by the open neighborhood N(v)N(v) - is at most 11, must GG be well totally dominated? Answered affirmatively; the Lean proof in fact needs only n≥2n\geq 2, and retains the conjecture's n≥5n\geq 5 to state the source faithfully.

Context

The formalization proves the statement under the weaker hypothesis n >= 2; the pull request marking the conjecture solved is open, not merged

Machine-generated (Written on the Wall II); real but unfamous by construction.

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

    proof attemptAristotle ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    Aristotle

    The pull request marking the conjecture solved credits the proof to Aristotle, Harmonic's prover; a human contributor prepared and filed the formalization.

    The formalization proves the statement under the weaker hypothesis n >= 2; the pull request marking the conjecture solved is open, not merged

    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

      Sorry-free Lean 4 proof filed against google-deepmind/formal-conjectures, which flips the conjecture's attribute from research open to research solved and links the proof. Unlike the site's WOWII 217 entry it needs no native_decide: the argument is conceptual, showing every neighborhood is a clique and deducing well-total-domination. Not independently reviewed, and the pull request is still open.

      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.