Topological θ-Sector in CPTP Dynamics: CP Violation from Measure, Not from Reweighting

We demonstrate numerically that θ-reweighting does not induce CP violation in CPTP (Completely Positive Trace-Preserving) ensem bles of quantum channels with a topological charge Q ∈ 1 2Z. When the underlying measure is CP-symmetric (P(Q) = P(−Q)), CP-odd observables vanish identically for any θ. Introducing an explicit CP asymmetry via eεQ yields a linear response A(π) ∝ ε with slope 0.132. We prove a theorem linking these observations and discuss the impli cations for the strong CP problem: CP violation is a property of the dynamical measure, not a consequence of post-processing reweighting.