Conjectured uniqueness of Brownian loop measure for SLE restriction
For every admissible central charge , the Brownian-loop measure is the unique loop measure whose associated restriction function satisfies the relevant conformal covariance, restriction, and local real one-dimensional modular-functor sewing axioms.
References
Primary source
Additional references
Progress summary
A new unrefereed paper claims uniqueness in a restricted setting, while independent confirmation and the broader conjecture remain outstanding.
The conjecture asks whether the Brownian-loop measure underlying SLE restriction is uniquely determined by the relevant conformal and modular-functor axioms. No proposer or original date is supplied in the scan.
Known results
- Baverez–Jego (July 2024) claim uniqueness of restriction measures for central charge , identifying them with loop measures.
- A February 2025 preprint claims uniqueness of Malliavin–Kontsevich–Suhov measures for .
- Zhan (2017) gives a rooted loop-measure uniqueness property under Möbius covariance and finiteness of large loops.
August 24, 2026 claimed uniqueness
On August 24, 2026, Universality of the conformal anomaly claimed to identify the disk–disk cocycle with loop Loewner energy and derive uniqueness within local real one-dimensional modular functors. The claim is unrefereed and restricted to that framework.
Current status (as of August 2026): Uniqueness is claimed within a restricted framework, but the claim is unverified and the full conjectural scope remains open.
Sources
- arxiv.org
- arxiv.org
- users.math.msu.edu
- math.uchicago.edu
- math.pku.edu.cn
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- yilwang.weebly.com
- quantamagazine.org
- deepmind.google
- quantamagazine.org
- arxiv.org
- arxiv.org
- mathstodon.xyz
- mathstodon.xyz
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- mathstodon.xyz
- quantamagazine.org
- quantamagazine.org
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