Signed BAR Conjecture for Reflected Brownian Motion
Does the finite signed basic adjoint relation determine the invariant signed measure uniquely, and how far beyond the Harrison-Reiman class can uniqueness extend?
- Result
- Proved(see note)
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Stochastic networks
- Posed by
- —
- Year posed
- 1990
- Years open
- 36y
- Solved
- 2026-07-03
- Model
- ChatGPT-5.5 Pro
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
uniqueness proved for stable Harrison-Reiman systems with a nonsingular M-matrix reflection; an infinite-dimensional obstruction is shown in the larger completely-S class
What the AI did
The pathwise-differentiability argument was developed in an AI-assisted collaboration; both authors verified the proof.
Verification
Two-author verification with a public arXiv proof. Not yet peer-reviewed.
Source
arXiv:2607.03639 - An AI-assisted solution to the signed BAR conjecture