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Most others say the standard reasoning holds, and the disagreement has not been settled.","posed_since":"2020","precise":"Determine whether CP-odd observables in QCD ($d_{n}$, the $\\theta$ dependence of the vacuum energy and of hadron matrix elements) depend on $\\theta_{\\mathrm{bar}}$ when the infinite-volume limit and the sum over topological sectors are taken in the order argued by Ai, Cruz, Garbrecht and Tamarit (arXiv:2001.07152). An answer is a proof or a lattice computation showing $d_{n}$ proportional to $\\theta_{\\mathrm{bar}}$, or the opposite.","problem_ref":null,"references":"","settled_by":"A rigorous treatment of the $\\theta$-dependence of CP-odd correlators in QCD, cross-checked by lattice computations of $d_n$ at imaginary or small real $\\theta$.","status_note":"Benabou, Hook, Manzari, Murayama and Safdi (arXiv:2510.18951, 2025) and Khoze (arXiv:2512.06827, 2025) argue $\\theta$ is physical; Ai, Garbrecht and Tamarit replied (arXiv:2511.04216, 2025) and the exchange continues in 2026 (arXiv:2601.18248); the majority view keeps the strong CP problem.","title":"Does a nonzero $\\theta$ produce observable CP violation in 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