Assumption: Structural class

Only the measurement transition varies. The admissible class has the following properties.

1. Qubit kinematics. For every finite live-name set $L$, states are unit rays in ${\mathcal{H}}_L$, with ordinary tensor composition.

2. Fixed coherent dynamics. All finite-register unitaries and fresh $|0⟩$ allocation act as in Layer I, with their stated linear-algebraic composition and tensor placement.

3. State sufficiency. The outcome law ${{\mathsf{P}}^{\mathsf{S}}}_{\psi }$ and positive-branch residual ray ${{\mathsf{U}}^{\mathsf{S}}}_{\psi }(\kappa )$ depend only on the current global ray and measured register, not on history, apparatus identity, or hidden memory.

4. Normalized laws and pure residuals. ${{\mathsf{P}}^{\mathsf{S}}}_{\psi }$ is a probability distribution on $\{0,1{\}}^S$. Each positive-probability outcome has a unit residual ray on ${\mathcal{H}}_{L\setminus S}$. Values on zero-probability outcomes are not part of the strategy.

5. Permutation equivariance. Consistent relabeling of names, tensor factors, measured positions, and outcome coordinates transports laws and residuals accordingly.

6. Unbounded finite resources. The strategy is defined at every finite size. Experiments may use any finite number of ancillas. Witnesses need not have the size of the system whose law is being characterized.

7. Evaluation convention. Single programs use left-to-right evaluation. Bipartite experiments interleave their local left-to-right executions. General liberal scheduler independence is not assumed.