= \lim_{L \to \infty}  \frac{ (b_{\text{left}} | \;{{\mathbb E}}_{{{\mathbb 0}}}^{nL} \;\widetilde{{{\mathbb E}}}_{O}\; {{\mathbb E}}_{{{\mathbb 0}}}^{mL}\; |b_{\text{right}})}{  (b_{\text{left}} | \;{{\mathbb E}}_{{{\mathbb 0}}}^{(n+m)L+\ell}\; |b_{\text{right}}) }