Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 230-02. An explicit exact Hausdorff gauge for SLE
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OpenAI@2026-10-07#rem:oai-p-230-02
Authors: OpenAI. Family 230.
Title: An explicit exact Hausdorff gauge for SLE.
Abstract: For each fixed $0{}lt {}kappa{}lt 8$, let $d=1+{}kappa/8$. The gauge $h(r)=r{}d({}log{}log(1/r)){}{(2-d)/2}$ at sufficiently small radii almost surely gives positive finite Hausdorff measure to every nontrivial positive-time compact segment of chordal SLEκ. This gives an explicit solution to Schramm's Hausdorff-measure problem in this parameter range. The entire trace has finite expected measure in every bounded disk. The exponent-one iterated-logarithm gauge suggested by Schramm is not sigma-finite on any such segment.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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