Low Homotopy and Noise-Stable Choi-Band Topology of Fixed-Kraus-Rank Quantum Channels

We determine a strict-interior low-homotopy window for finite-dimensional exact-Kraus-rank CPTP channel manifolds, treat feasibility and boundary branches, identify low-stage Choi-support Chern invariants, construct a trace-preserving qubit S4 Yang-monopole channel with |c2|=1, and extend the topology to isolated full-rank Choi spectral bands under gap-preserving perturbations. We also prove finite-node non-identifiability of continuum c2 over unrestricted smooth gapped families and give conditional data-side and holdout subspace certificates. The four-dimensional numerical route retains full non-Abelian U(r) overlap information and distinguishes the trace-curvature invariant from the mathematical second Chern class, including the Chern-Weil c1^2 correction required for general U(r) bundles.