Papers CCXXXIII and CCXXXIV identified the ringdown mode content of binary black hole mergers as the Akivis–Mal'tsev BCH commutator tower of two coalescing G2-valued infundibulum connections, deriving six zero-parameter predictions against the Dyer clean Fano-line selection for the four predicted quadratic modes with zero non-Fano detections; retrograde-mode prevalence in anti-aligned spin configurations at a factor of 4. 7× over aligned/nonspinning baselines). The fourth (Cartan-height overtone truncation of CCXXXIV Lemma) confirms only after one structural refinement: the free e7 contribution is universal across all (I, I) towers, not localized to (6, 6), giving the corrected prediction nmax=6 universally. Phase 2 (the quantitative η3=1. 255% cubic-to-fundamental amplitude ratio and the A (I, I, 0) /A (2, 2, 0) tower) requires running bgpqnmfits against SXS CCE waveforms; the scaffold is in place and results will follow in Paper CCXXXVI. 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.
Bharathi Jagadeesan (Tue,) studied this question.
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