Sign Reversal in the Eccentricity Dependence of the (2,1) Gravitational Wave Mode: Evidence for a Two-Channel Coupling Mechanism and Toroidal Projection Factor in Binary Black Hole Ringdown

The (2,1) gravitational wave mode is predicted to vanish in symmetric binary black hole systems under general relativity. We report a sign reversal in its eccentricity dependence across 83 numerical relativity simulations from the SXS catalog: the full population shows a negative correlation (α = −0.65, p = 0.0003), while the symmetric subsample (q ≈ 1, χ ≈ 0) shows a positive correlation (γ = +0.43, Mann-Whitney p = 0.043). The (2,0) control mode shows negative correlation throughout, confirming the result is mode-specific. A single GR mechanism cannot produce both signs. We propose a two-channel model in which all matter is asymmetric substrate and eccentricity is the accumulated coupling receipt of the orbital geometry's history. We introduce IE-002, the Toroidal Projection Factor F = α·(R/r − 1), derived from Kerr horizon geometry. IE-002 achieves R²_adj = 0.834 as a standalone predictor and R²_adj = 0.917 in an interaction model (p < 0.0001). The model predicts h₂₁ ≥ 9×10⁻⁹ at e = 0.001, q = 1.000, χ ≈ 0 — a non-zero floor that GR requires to be zero. This is GCT Paper 40 of 49.