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OpenAI reports: Kaplansky zero-divisor counterexamples

OpenAI reports a finitely presented torsion-free group with a finite two-dimensional classifying space whose group algebra over the two-element field contains nonzero elements with product zero.

Sources for this record

What was already known

Torsion gives elementary zero divisors. Kaplansky’s conjecture instead asks whether removing torsion suffices; positive results for particular torsion-free classes do not settle that universal assertion.

What changed and why it matters

Refutes the stated zero-divisor conjecture while retaining torsion-freeness and finite presentation.

The AI contribution

OpenAI attributes these manuscripts to its internal model. The entry does not infer individual human contributions beyond that publisher attribution.

Limitations

The construction is in characteristic two. It does not establish a counterexample over every field, and it is distinct from the separate direct-finiteness claim. Preprint. This is a source-statement and significance assessment, not a proof audit. No independent checking or successful formal compilation is asserted by this entry.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The publisher reports the scoped result. AIProofWatch has not independently validated its correctness.

Accessible artifact / proof

The original written argument is accessible. Availability does not establish a successful proof check or Lean verification.

Correction and publication history

2026-10-11 · publication

Historical report added after statement, scope, and importance review. No proof audit or formal checking asserted; subscriber alerts disabled.

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