OpenAI reports quenched SLE₃ convergence for weak random-bond Ising interfaces

For planar Ising bonds J_e=1+εξ_e with any fixed bounded, nondegenerate, mean-zero iid disorder law and sufficiently small ε>0, the full oriented interface law at the spontaneous-magnetization threshold converges in probability over environments to chordal SLE₃ in deterministic Jordan-domain approximations.

Sources for this record

What was already known

Chordal SLE₃ convergence was known for the pure square-lattice Ising spin interface; earlier random-bond work did not establish this quenched whole-curve limit for general bounded weak disorder.

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

Extends conformal interface universality to weak random-bond Ising models in the quenched sense.

Limitations

The disorder must be bounded, iid, mean-zero, and weak enough for its law. The Lean scope checks a finite-graph Ising likelihood-ratio comparison, not the random-bond critical point or quenched SLE₃ convergence.

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, prior-work, and precise Lean-scope or conditional-input review for non-notifying local inclusion.

Read this published revision