Huneke-Wiegand Conjecture

Precise statement

The Huneke–Wiegand Conjecture: Let $R$ be a one-dimensional Gorenstein local domain, and let $M$ be a finitely generated, non-zero, torsion-free $R$-module. If the tensor product $M \otimes_R M^*$ is torsion-free, then $M$ is a projective (hence free) $R$-module.

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

GPT-5.6-Pro

Came up with the counterexample on shot. GPT-share chat for proof: https://chatgpt.com/c/6a6529a6-fb04-83ea-a397-a64ffed0b3d6

Provider: unknown · Prompt public: unknown · Independence: unknown

Verification boundary

independent expert verified

The proposed data are: Γ = ⟨56,57,58,63,64,70,71,72,73,74,75,76,77,78,79,80,81,82,83, 87,89,90,93,95,96,97⟩, R = ℚ[t^Γ]_𝔪 I = (t^56,t^70)R Full link: https://github.com/sonpham-org/huneke-wiegand-candidate-verification Contains my own counter example proof and an independent verification by the conjecture author

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

Timeline

1. 2026-07-29

   GitHub

   Verified by author of the conjecture

Known method families

construction (source-reported)

Source-reported tools: construction.

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.