Track A5: complete-process identification

For reduction-only dynamics on the two-dimensional code, let $L=\sqrt{R/2}Z$. Both

and

have ensemble generator ${\mathcal{D}}_L$. The second process preserves norm by Itô's rule. Its branch populations are bounded martingales, and for $V={\mathrm{Var}}_{\psi }(Z)$,

For $R>0$, population convergence and finite $\mathbb{E}{{\int }_0}^{\infty }{V}^{2}dt$ force $V\to 0$; the selected code vertex has its initial population as probability. The random-unitary process instead preserves those populations trajectory by trajectory.

They nevertheless have identical complete system-only records if each conditional interval is specified by the same Markov channel and the hidden noises are inaccessible. This conclusion uses Theorem thm:process, not one-time equality alone.