OpenAI reports SLE limits for square-lattice random-cluster interfaces

For each fixed 1≤q<4, the critical square-lattice random-cluster Dobrushin interface converges as an ordered curve in uniformly approximated marked bounded Jordan domains to chordal SLE with κ(q)=4π/arccos(−√q/2).

Sources for this record

What was already known

The FK-Ising q=2 interface limit was known, while general q rotational-invariance work did not identify the interface law. The manuscript acknowledges overlapping public q=1 square-lattice percolation claims.

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

Identifies the full interface scaling law across the critical square-lattice random-cluster range 1≤q<4.

Limitations

This selected contribution is the Dobrushin interface limit; nested whole-plane loop convergence is a separate claim. q=1 and q=2 have prior or overlapping results, so novelty lies in the general parameter range and stated domain scope. 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.

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