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OpenAI reports: The even-periodic spin-one Haldane gap

OpenAI reports a uniform positive spectral gap above the ground energy for the pure antiferromagnetic spin-one Heisenberg chain on even periodic rings.

Sources for this record

What was already known

Evidence for a gap in finite samples or a different spin-chain Hamiltonian does not establish a length-uniform gap for the pure bilinear spin-one model.

What changed and why it matters

Establishes the stated uniform-gap formulation for the pure even-periodic spin-one chain.

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 entry covers even periodic rings and the stated pure Hamiltonian. Different boundaries, odd lengths, and perturbed models require separate statements. 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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