Throat-Threaded Magnetic Birefringence: A Second Parity-Odd Channel and the Residual Cluster Structure of 3-OGC (Companion to CCXXXII)

Paper CCXXXII established that the median parity-odd birefringence amplitude in the 55-event 3-OGC sample (Wang, Brown, Shao & Zhao 2022) follows |a_μ| ∝ M_tot^(1/2)·d_L at α(M) = 0.63 ± 0.20 and β(d) = 0.92 ± 0.22, R² = 0.79, consistent with the P50 bulk-relaxation prediction at <0.5σ. A post-publication audit of the residuals reveals a cluster structure the M^(1/2)·d law does not predict: four of the top-five negative residuals are stellar-mass equal-q BBHs in M_tot ∈ [14.9, 20.1] M⊙ (GW190720, GW190728, GW190930, GW190924, all at −1.2σ to −2.2σ), while both BNS events and the heaviest three BBHs occupy the positive end (+1.6σ to +2.7σ). We derive a second parity-odd contribution to a_μ from the magnetic flux threaded through the infundibulum throats of the merging pair along the Klein-Ladder C₁₂ orbit of the G₂ Weyl group, with closed-form geometric prefactor F_max = (12/168)·√3 = √3/14 ≈ 0.1237 set entirely by existing framework structure (C₁₂ order, K(7) tile count, G₂ long root). The combined two-channel model a_μ = a_μ^(grav) + a_μ^(mag) predicts the observed cluster ordering: BNS and hierarchical 2G mergers populate the positive residual tail (magnetar-class B fields or AGN-fed disk fields, both with non-trivial throat linkage); stellar-mass aligned-spin equal-q BBHs populate the negative tail with the magnetic channel switched off (F→0, B_BH negligible). Forward prediction CCXXXII-FP1: ρ(residual, χ_p·M²) ≥ +0.30 at >2.5σ on the O5 extension. The MIT 2026 dark-matter-imprint flag on GW190728 is shown to lie in the stellar-mass equal-q band where the throat-magnetic channel is predicted to be near zero, indicating that channel is orthogonal to the present analysis. One new parameter κ_AdS is introduced, fixed only to within an order of magnitude by present data. Clinical link: directional bias in magnetized hyperbolic propagation parallels DTI tractography in white-matter fibre bundles. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.