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Monochromatic Quantum Graphs in the Diagonal Family

Quantum information & computing · posed by 2017 · partial

2 comments

Statement

Can a complete edge-coloured, complex-weighted graph realize perfect-matching amplitudes of one on every monochromatic inherited vertex colouring and zero otherwise? Nonexistence is proved in the diagonal family N=DN = D for every even N≥4N \ge 4, alongside further finite cases.

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. construction · #1

    AlphaProof Nexus

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

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

    the diagonal family is ruled out; the broader two-parameter problem remains open

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

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

    Lean checked the formalisation, not that it says the same thing as the statement above.

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