Parity symmetry as a diagnostic for spin-precessing binary-black-hole waveform models

Parity invariance of general relativity imposes exact relations between waveforms and remnant properties of binary-black-hole configurations related by reversal of the in-plane spins and observer direction. We summarize these relations and construct consistency tests for spin-precessing waveform and remnant models. Applying a conservative, unmaximized overlap diagnostic to seven state-of-the-art waveform models, we find that models built from aligned-spin calibrated waveforms and parity-covariant precession dynamics satisfy the symmetry to numerical precision. The original $\mathtt{\text{IMRPhenomXO4a}}$ and $\mathtt{\text{IMRPhenomXPNR}}$ implementations instead exhibit median parity residuals of approximately $1.6\times {10}^{-3}$ with broad upper tails, while $\mathtt{\text{NRSur7dq4}}$ shows its largest violations at high mass ratio and large spin magnitude. The asymmetric extension of $\mathtt{\text{SEOBNRv5PHM}}$ exhibits a smaller, localized violation, while $\mathtt{\text{NRSur7dq4Remnant}}$ shows larger residuals in the recoil than in the final mass and spin. We trace these violations to an observer-dependent phase anchor in the $\mathtt{\text{IMRPhenom}}$ antisymmetric mode, non-invariant parameterization of the $\mathtt{\text{NRSur7dq4}}$ surrogate fits, and one non-invariant NR-calibrated coefficient in the asymmetric $\mathtt{\text{SEOBNRv5PHM}}$ extension. Local corrections restore waveform parity to numerical precision for the $\mathtt{\text{IMRPhenom}}$ and $\mathtt{\text{SEOBNRv5PHM}}$ cases; restoring it in $\mathtt{\text{NRSur7dq4}}$ requires refitting the surrogate. Reanalyses of eight GWTC-5.0 events show no qualitative change in astrophysical interpretation, although the $\mathtt{\text{IMRPhenom}}$ correction yields Jensen-Shannon divergences up to $5\times {10}^{-2}$ in individual marginalized posteriors. Exact symmetries thus provide inexpensive, model-independent consistency tests and should be imposed by construction in calibrated waveform models.