The Signed BAR Uniqueness Problem
Statement
For a multidimensional reflected diffusion, does the basic adjoint relationship uniquely characterize the stationary distribution? The question had stood unresolved for more than thirty-five years since the BAR approach was introduced. For stable Harrison-Reiman data with a nonsingular -matrix reflection matrix, the finite-signed uniqueness problem is settled, via pathwise differentiability of the reflected process; the nonsigned version is also shown unique within the Harrison-Reiman class.
Record
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Yiping Lu and Youheng Zhu, using ChatGPT 5.5 ProThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The paper names the model contribution in its title and states that the proof was discovered with the assistance of ChatGPT 5.5 Pro and subsequently verified by the authors, with the chat logs published. It also records a negative result worth having: on a harder related task both ChatGPT 5.5 Pro extended and Claude Opus 4.8 max failed.
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