Corollary: A controlled large-dimension scaling

Take $L_n=\lceil an\rceil$, $t=n{t}_0$, and $q_n=2^{k_n}$ with

Choose $a$ to make the escape allowance vanish. Then the random-Clifford support at time $n{t}_0$, and its normalized annealed OTOC levels, have limiting body $t_0\mathcal{B}$ in probability. Regularity remains conditional on hyp:exp.

Proof. Here $M_{L_n}=O(n^2)$, so the coupling allowance is $O(n^3/{q_n}^2)=o(1)$. Add the exponentially small escape allowance. On the resulting common good event the complete support history equals the confined FPP history. Apply the shape theorem and Theorem thm:transfer.