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Quantum-classical transition. Construct an explicit RBDS morphism between the quantum measurement RBDS and the classical TM RBDS, with decoherence as the resource bound.
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Computational complexity of distinctions. For an RBDS $\mathcal{D}$, define $\mathrm{DC}(\mathcal{D}) = $ minimum budget required to realize a given distinction.
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RBDS cohomology. Define $H^n(\mathcal{D})$ whose classes correspond to obstructions to realizability.
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Continuous RBDSs. Replace $X$ with a topological space and $\Pi_B$ with a continuous idempotent. Connection to Krein spaces.
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Higher RBDSs. Replace the operational monoid with a monoidal category.
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Observation Monad and Functor $\mathcal{F}: \mathbf{Cat} \to \mathbf{Dyn}$. See §8.
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Conjecture 7.1 (Macroscopic limit of state-dependent open quantum systems). Let $\{L_k(\rho)\}$ be Lindblad jump operators depending smoothly on the quantum state $\rho$. Under appropriate scaling ($\hbar \to 0$, $N \to \infty$, or weak-coupling limit), the resulting open-system dynamics admits a classical limit described by the witness-graph ODE $\dot{x} = F(x, A(x))$ with the dissipator's drift generating $F$. Requires a rigorous limit theorem not provided here. See §7.8.