OpenAI reports a CLE₄ curve limit for half-plane double dimers

The complete loop ensemble of the Temperleyan square-lattice double-dimer model in the upper half-plane converges along the full mesh limit to nested CLE₄, matching every macroscopic loop as an unparametrized curve.

Sources for this record

What was already known

Kenyon’s dimer-height convergence to the Gaussian free field supported the CLE₄ prediction but did not itself establish convergence of loop curves and their nesting.

AI involvement AI-led

OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.

OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.

Importance Major

Resolves the half-plane Temperleyan double-dimer CLE₄ scaling-limit conjecture at the level of complete curves.

Limitations

The result is for the specified half-plane Temperleyan square-lattice model, not every double-dimer boundary condition or planar graph. No completed proof check was documented in the available sources.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.

Correction and publication history

2026-10-18 · publication

Primary manuscript, attribution, and prior-work review for non-notifying local inclusion; technical check remains undocumented.

Read this published revision