Paper CCXXXV of the One-Octonion Brane-Bulk Series Preliminary Empirical Confirmation of the Akivis–Mal'tsev BCH Ringdown Predictions (Papers CCXXXIII + CCXXXIV) against the Dyer & Moore (PRL 136, 191403, 2026) Public

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 & Moore (2026) public catalog. This short note reports Phase 1 of that verification: the four structural predictions that can be tested from per-simulation mode-detection JSONs alone, without re-running Bayesian amplitude fits. Of these, three confirm cleanly in their original form (cubic-mode detection localized to fits including the (6,6) target harmonic; 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 bgp_qnm_fits 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.