Uniform real Lipschitz surfaces on the triangular lattice

OpenAI

For uniform real nearest-neighbor Lipschitz heights on triangular-lattice approximations of smooth simply connected domains, the October 6 manuscript claims a centered and normalized Dirichlet Gaussian free-field limit. With a tuned opposite two-arc boundary amplitude, the zero-height interface converges to chordal SLE₄ in uniform curve distance.

Sources for this record

What was already known

Schramm’s Problem 2.3 predicted these field and interface limits. Related integer-height papers concern different models and boundary data.

AI involvement AI-led

OpenAI credits an internal model with producing its manuscript collection. No proof-specific account establishes task-only autonomy, and no human checker or explainer is named for the revised real-height argument.

OpenAI authorship and its model-production disclosure support model-led central work, without a contribution-specific autonomy account for the revised proof.

Importance Notable

The paired limits answer Schramm’s problem for the stated real-height model and boundary conditions.

Limitations

The October 6 revision repairs boundary attachment, landing comparison, multiscale separation and whole-curve arguments in an earlier version. No completed check of the revised proof is documented; broader domains and boundary amplitudes are not claimed.

Technical verification Reported

The October 6 paper is an unformalized manuscript in the release; the source does not document a completed check of its real-height field and SLE4 interface arguments. The explicit repairs show why the older September 25 version must not be treated as the assessed proof.

Human understanding Few

No documented human explanation of the central scaling and whole-curve mechanism was found. Few is the evidence default, not a finding that researchers cannot explain it.

Correction and publication history

2026-10-18 · publication

If correct, the paired limits answer Schramm’s problem for the stated real-height model and boundary conditions.

Read this published revision