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Log-Concavity of Codimension-Three Pure O-Sequences

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pure-o-sequences-log-concavityAlgebraposed by 2022recorded: solved

1 attempt · 1 machine check · no person has looked

Statement

For a pure O-sequence h=(h0,…,he)h = (h_0, \dots, h_e) of codimension three and type two, is hi2≥hi−1hi+1h_i^2 \ge h_{i-1} h_{i+1} for every interior index ii? The stated monomial case is proved; the broader level-Hilbert-function case remains open.

Context

An explicit conjecture inside the pure O-sequence program.

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Attempts

1 attempt

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  • #1

    Attempt 1

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

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

    Reviews

    0 human reviews · 1 machine check

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    • 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) and its accompanying repository.

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    Discussion of this attempt

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Discussion

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