What was already known
Beffara identified the trace dimension, Rezaei showed the critical power gauge gives zero measure, and Schramm asked whether a deterministic gauge could give a sigma-finite trace measure.
AI involvement
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
Answers Schramm’s Hausdorff-measure existence question for chordal SLE with 0<κ<8.
Limitations
The manuscript constructs a gauge via deterministic moment integrals. The Lean scope checks positivity for a later explicit gauge, but not finiteness for every segment or the first manuscript’s moment-integral construction.
Technical verification
OpenAI reports a Lean check of a narrower theorem, case, or component; the selected claim extends beyond that scope.
Formal checking
The pinned OpenAI Lean scope note verifies only this narrower statement, not the full selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For 0<κ<8, the explicit gauge r^d(log log(1/r))^{(2-d)/2}, d=1+κ/8, gives positive measure to every nontrivial compact positive-time chordal SLE_κ segment.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
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
Primary manuscript, attribution, prior-work, and precise partial or mismatched Lean-scope review for non-notifying local inclusion.
Read this published revision