Systematic Source-Parameter-Dependent Bias in Numerical-Relativity Ringdown Extraction: Evidence from a Kerr Coordinate Benchmark

Numerical-relativity ringdown extraction pipelines carry a systematic +8.4% positive bias in Q220 relative to exact Kerr predictions, with Pearson correlation r=+0.437 (p<0.001) with progenitor aligned spin χ1z. This bias is not removed by standard selection cuts. On the exact Kerr control benchmark, (1−af)−0.50 best linearises Q220, while 1/κM is the leading coordinate for the pure damping rate τ220/Mf. On the NR pipeline benchmark, κM gives the lowest LOOCV RMSE among three pre-registered coordinates (stable under blocked validation, leverage removal, and spin-weighting), but the discrepancy with the exact Kerr ranking identifies this advantage as pipeline-mediated rather than a property of the Kerr spectrum. 382 SXS binary black hole simulations analysed. All data and scripts publicly available. Companion documents: Transformer Boundary Case (pub-018) Bridge Synthesis (pub-021) Fixed-Point Theorem (pub-010)