Theorem: Inhabitation

The Born strategy belongs to the structural class and satisfies $(\mathrm{C}{)}^{\star },(\mathrm{NS}{)}^{\star },(\mathrm{N}{)}^{\star },(\mathrm{K}{)}^{\star },(\mathrm{R}{)}^{\star }$.

Proof. The formulas give normalized laws and pure residual rays, are state sufficient and phase invariant, and are equivariant under consistent name and tensor permutation. They are defined at every finite size with the fixed coherent dynamics and evaluation convention.

Composability is Lemma lem:concrete-C. No-signaling is Theorem thm:internal-ns. A zero destructive component has zero squared norm, proving nullity. Each squared norm is continuous, and there are finitely many outcomes, proving continuity. Proposition prop:concrete-record proves records.