Validated Parity-Odd Estimators as Control Diagnostics in Faraday Rotation Measure Studies

Parity-odd statistics are frequently invoked in Faraday rotation measure (RM) analyses as potential indicators of magnetic helicity or chirality. However, such statistics are particularly susceptible to estimator bias, sampling geometry, and survey systematics. We present and validate a parity-odd handedness estimator designed explicitly as a control diagnostic, not as a signal detector. The estimator is constructed to invert under spatial mirroring and to vanish under randomization, enabling direct testing for spurious asymmetries. Applying the diagnostic to the LoTSS DR2 RM Grid, as implemented in Doumbouya (2026), we demonstrate the absence of statistically significant global or high-latitude magnetic handedness and identify predictable scale-dependent degradation due to finite sampling. We emphasize that parity-odd estimators of this class should be treated as null tests that establish symmetry baselines, protecting subsequent structure analyses from false parity claims.