Left-right symmetric theories with generalized parity restrict the bare QCD angle to a $CP$-conserving value and relate the physical strong-$CP$ phase $\overline{\theta }$ to a $CP$-odd parity-breaking parameter $\epsilon$. We show that, in the Dirac-neutrino realization, imposing a sectorial reality condition on the Dirac lepton Yukawa matrices turns observable leptonic $CP$ violation from an independent input into a branch-dependent prediction. Parity reconstructs the right-handed leptonic mixing matrix, whereas leptonic reality requires it to be rephasing-equivalent to the complex conjugate of the left-handed one. For generic three-generation Yukawas, compatibility is equivalent to the vanishing of a single Jarlskog-type $CP$-odd invariant. In the physical Dirac hierarchy, for fixed oscillation data, mass ordering, and discrete leptonic branch, compatibility determines the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) Jarlskog invariant as a function of the lightest neutrino mass and $\epsilon$. We derive its leading analytic behavior and obtain the nonlinear compatibility branches numerically. In compressed mixed-sign Dirac-neutrino spectra, small signed mass sums can amplify a tiny parity deformation into order-one values of the normalized PMNS Jarlskog invariant, including maximal $CP$ violation. The corresponding quark reconstruction independently provides a calculable, branch-dependent conversion between $\epsilon$ and $\overline{\theta }$. Together, the leptonic and quark relations define a family of correlations among leptonic $CP$ violation, the absolute neutrino mass scale, and strong $CP$.

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• Extensions of gauge sector
• Neutrino mixing
• CP violation
• Neutrino mass
• P-symmetry