Log-Concavity of Codimension-Three Pure O-Sequences

Precise statement

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

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

AlphaProof Nexus

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

Provider: Google DeepMind · Prompt public: unknown · Independence: unknown

Verification boundary

lean verified statement audited

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

Correctness: supported · statement fidelity: audited · peer review: none

Timeline

1. 2026-05-21

   arXiv:2605.22763 - AlphaProof Nexus report

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.