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Breakthrough Tracker record

An AI-assisted explicit ideal is claimed to disprove the general Huneke–Wiegand conjecture

Son Pham constructs a one-dimensional Gorenstein local domain and a nonprincipal two-generated ideal whose tensor product with its dual is torsion-free, giving a counterexample to the conjecture's general Gorenstein formulation over every field.

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Stable ID
math-huneke-wiegand-counterexample-2026
Revision
math-huneke-wiegand-counterexample-2026.v1
Field
Mathematics · Commutative algebra, Gorenstein rings and exact finite verification
Evidence
Tier 1 · Peer reviewed: No
Record state
Provisional · Provisional; independently recomputed example
Last checked

AI role

The author says GPT-5.6 Pro assisted the search, early drafting and initial verification code, and that ChatGPT assisted the exact checks and preparation of the submitted version.

Record details

Problem or result
The general one-dimensional Gorenstein Huneke–Wiegand tensor-product conjecture
Authors
Son Pham
Institutions
Independent researcher
Result date
Preprint submitted September 7, 2026

Why it matters

The conjecture has shaped rigidity questions in commutative algebra since the 1990s. The explicit numerical-semigroup example supports both algebraic proofs and small exact certificates.

Limits

The manuscript has not been peer reviewed. Craig Huneke is reported to have independently recomputed the semigroup and colon-ideal data and verified rigidity, but the tracker has not independently run the two supplied Python verifiers. The counterexample does not cover complete-intersection restrictions.

Sources

  1. Primary: Pham, Huneke–Wiegand counterexample
  2. Independent context: Christensen, Gerko and Iyengar, related rigid-ideal construction

Correction and revision history

  1. 2026-09-10 — Added after primary-source, scope, status, AI-role and limitation review.

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