Paper CCXXXIII of the One-Octonion Brane-Bulk Series Ringdown Mode Content as the Akivis–Mal'tsev BCH Commutator Tower of Coalescing G2 Infundibula:

Dyer & Moore (PRL 136, 191403, 2026) present a fully Bayesian, data-driven identification of quasinormal mode (QNM) content in high-fidelity SpECTRE Cauchy characteristic evolution (CCE) ringdown waveforms. They confirm overtones to n=6, quadratic nonlinear modes, retrograde modes prominently in component-spin anti-aligned configurations, and a stable cubic QNM (2,2,0,+)3 in the (I,m)=(6,6) harmonic. We show that this entire hierarchy is the Akivis–Mal'tsev extension of the Baker–Campbell–Hausdorff (BCH) composition of two coalescing κ=−1 hyperbolic infundibula (Papers CXXIX, CXLVIII, CL, CLXII), each described by a G2-valued brane connection. The mapping is: BCH commutator depth k ↔ QNM radial overtone index n; nested Lie-bracket structure ↔ quadratic and higher multi-mode sourcings; octonion associator [e4,e5,e6]=−2e7 (Paper CVIII) ↔ the cubic mode (2,2,0,+)3. Five zero-parameter predictions follow: (CCXXXIII-1) the cubic-to-fundamental amplitude ratio is the non-associative three-body coupling K/J = n·fbulk = 1.255% already derived in Paper CXCVIII; (CCXXXIII-2) quadratic mode amplitude ratios follow the Fano-line incidence structure constants 2εijk; (CCXXXIII-3) the overtone tower truncates at nmax=5 from the G2 Cartan depth, with an n=6 recurrence corresponding to the free e7 radial breathing mode of Paper CCXIII; (CCXXXIII-4) retrograde-mode amplitude in anti-aligned-spin binaries scales as sin2(θmisalign/2) from H+/H− ordering reversal (Paper CXLIX); (CCXXXIII-5) the framework predicts a late-time power-law tail of amplitude ∝ a0·M·t in Cauchy-characteristic matching simulations, pre-registered before any such catalog publishes such a measurement. The paper closes a triangle between Paper CCIX (BCH Taylor expansion of spacetime), Paper CCXIII (Onsager {6,3} disk lock-in), and the GW birefringence prediction of Paper CCXXXII into a unified Lie-algebraic description of ringdown. 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.