Double-exponential escape conjecture for shortest exploding paths

Let $\gamma_{0}^\star=(0,v_1^\star,v_2^\star,\dots):=\arg\min\{\lvert\gamma_L\rvert\}$ be the shortest exploding path starting at $0$, where $\lvert\gamma_L\rvert$ denotes its $L$-length. Double-exponential escape conjecture. There exists some $b>1$ such that

$$\|v_n^\star\|\geq\exp\{b^n\}.$$

The conjecture predicts that a shortest exploding path jumps toward infinity at least double-exponentially fast. The supplied text gives no resolution.