What question did this study set out to answer?

This research aims to empirically confirm predictions about the ringdown modes of binary black hole mergers derived from theoretical models.

June 12, 2026Open Access

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

Key Points

This research aims to empirically confirm predictions about the ringdown modes of binary black hole mergers derived from theoretical models.
Phase 1 verification used per-simulation mode-detection JSONs without re-running Bayesian amplitude fits.
Observed cubic-mode detection and Fano-line selections in simulations. Quantified mode prevalence in spin configurations.
Confirmed three structural predictions: cubic-mode localization in (6,6), Fano line selections for quadratic modes, and retrograde prevalence over 4.7× for anti-aligned spins.
Fourth prediction refined to confirm universal free e7 contribution after adjustments, leading to a corrected prediction of nmax=6.

Abstract

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.

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