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

Compares physically motivated Kerr coordinates for parameterizing quasinormal-mode damping Q220 in binary-black-hole merger remnants using 382 numerical-relativity simulations from the SXS catalog. Among three pre-registered physical coordinates—raw spin af, horizon angular velocity ΩHMf, and dimensionless surface gravity κM—surface gravity gives the best out-of-sample performance under leave-one-out cross-validated RMSE. A simple linear model in κM approaches the performance of standard transformed-spin baselines while retaining direct physical interpretation. Selection-bias analysis confirms the coordinate ranking is stable across remnant-spin subsets. Terminology. The foundational publications developed the framework under the name Harmonic Coherence, reflecting its origin in physics domains where phase-locked resonance and coherent-structure formation are the operative bridge mechanisms. As the framework extended to number theory, complexity theory, and algebraic geometry—domains with no physical harmonic content—the name became a source of friction. This paper uses Hierarchical Compression (HC) for the domain-independent Layer 1 framework and reserves Harmonic Coherence (always spelled out, never abbreviated) for the Layer 2 physics-domain bridge instantiation. The abbreviation HC refers exclusively to the framework. Companion documents: Fixed-Point Theorem | Transformer Boundary Case | Bridge Synthesis