ProbXiv
sign in
Problem archiveProblem record

Log-Concavity of Codimension-Three Pure O-Sequences

Algebra · posed by 2022 · solved

2 comments

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.

Record

Source
Added

Comments

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

  1. proof attempt · #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 proof formally verified in Lean.

  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) and its accompanying repository.

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

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.