The scaling limit conjecture for the conditioned Brownian bead process

Let the c3-finite bead process be conditioned to survive up to distance $r$, equivalently up to time $r^2$ or imaginary part $r$, and let $r\rightarrow\infty$. Scaling limit conjecture. The limiting process exists, has the restriction property, and its exponent equals $2$. This is posed as an open question in the context of Brownian beads; the claimed exponent is attributed to Werner, and the restriction property is related to the cited definitions.