What was already known
A published OpenAI record covers the September 25 existence result using a deterministic moment-integral gauge. Earlier work established dimension d and zero measure for the critical power gauge r^d.
AI involvement
OpenAI credits its internal model with both manuscripts. No named human checker or explainer of the full explicit-gauge theorem was documented.
OpenAI authorship and the cited production disclosure establish central internal-model work; autonomy of this individual result is not documented.
Importance
The later manuscript supplies a simple explicit formula for the gauge, beyond the published existence result.
Limitations
Lean checks a lower-positivity target for the explicit gauge, not the finite upper-measure or expectation claims. The two papers do not show their gauges are asymptotically equivalent.
Technical verification
The cited Lean target proves a lower-positivity proposition conditional on its definitions of ordinary chordal SLE and the explicit gauge. It does not state the finite-measure upper bound, expected bounded-disk measure, or the moment-defined companion gauge. No completed check of the full theorem is documented.
Formal checking
Lean proof of lower positivity for the explicit gauge
- Checker
- Lean 4 kernel, as reported by the OpenAI repository
- Scope
- Positive Hausdorff gauge measure of each positive-time chordal SLE segment for the explicit formula under the formalized definitions
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explains the dense-visit, stopped-law and arbitrary-cover mechanism; Few is the evidence default.
Correction and publication history
The later manuscript supplies a simple explicit formula for the gauge, beyond the published existence result.
Read this published revision