ProbXiv
sign in
machine only

Four-Particle Monochromatic Quantum Graphs

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.

monochromatic-quantum-graphs-four-particlesQuantum information & computingposed by 2017recorded: partial

1 attempt · 1 machine check · no person has looked

Statement

For four particles and local dimension D≥4D \ge 4, can a complete edge-coloured, complex-weighted graph have unit perfect-matching amplitude for every monochromatic inherited colouring and zero for every nonmonochromatic one? Ruled out for the whole family, including the real-, integer- and trinary-weight variants.

Context

the N = 4, D ≥ 4 family is fully ruled out; the general two-parameter problem remains open

From the quantum-graph existence program of Krenn's 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

    constructionAlphaProof Nexus ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    AlphaProof Nexus

    Solved autonomously by AlphaProof Nexus, with the proofs formally verified in Lean.

    the N = 4, D ≥ 4 family is fully ruled out; the general two-parameter problem remains open

    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

      Lean-checked; formal proofs published with DeepMind's AlphaProof Nexus report (arXiv:2605.22763).

      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.