Born Measurement Contexts from Flows: Flows and Measurement Contexts in a Reconstruction of the Born Rule: Finite Commutator Closure and a Complex-Type Criterion

We consider finite families of projective measurement contexts transported by orthogonal flows on a finite-dimensional real Hilbert space. Their linear orbit is recovered by an iterated commutator closure, which stabilizes after finitely many steps and has the same commutant as the full continuous orbit. A finite family of transported projections then provides a computable witness for the generated algebra, its irreducibility, and the real, complex, or quaternionic type of its commutant. Singular-value gaps give quantitative control of approximate commutation and stability under perturbations. We also construct flow families realizing the complex branch, including graph-based modal generators and finite witnesses with repeated spectral gaps. The result isolates the intermediate regime relevant to the Born reconstruction: the context family is irreducible while retaining a two-dimensional neutral commutant whose skew-adjoint direction determines a common complex structure.