What question did this study set out to answer?

The primary aim is to investigate the cubic quasinormal mode amplitude predictions and their validation through direct measurements, correcting prior assertions.

June 17, 2026Open Access

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

Key Points

The primary aim is to investigate the cubic quasinormal mode amplitude predictions and their validation through direct measurements, correcting prior assertions.
Direct measurement on the Dyer & Moore CCE catalog (identified with SXS:BBH_ExtCCE:0010/0011/0012).
Validation of predictions against known quadratic modes and establishing a hierarchical structure in ringdown analysis.
Utilization of Bayesian data-driven identification methods for quasinormal mode content.
The cubic amplitude prediction was corrected from 1.255×10⁻² to approximately 0.595, fitting within the expected range.
Confirmed overtones extend to n=6, with cubic modes and retrograde configurations observed in specific spin states.
Five zero-parameter predictions were established regarding amplitude ratios, truncation indexes, and scaling laws for retrograde modes.

Abstract

v2 (2026-06-14) — ERRATUM appended. The headline cubic-QNM amplitude prediction η₃ = |C (2, 2, 0) ³|/|C (2, 2, 0) |³ = n·fbulk = 1. 255×10⁻² is FALSIFIED by direct measurement on the public Dyer single power of fIII = coherence, the same Born-once principle that fixes fIII in the neutrino sector; bulk fraction via the H⁻ associator e4, e5, e6=−2e7 → e7). The cubic is the unique framework nonlinear mode; quadratics are incomplete (2-of-3-dimension) projections = ordinary GR mode-coupling, carrying no framework prediction. The cubic mode’s existence and (6, 6) localization, the Fano quadratic selection rule, the retrograde-spin rule, and nₘax stand. See appended erratum + correction note. v2 (2026-06-14) — ERRATUM appended. The headline cubic-QNM amplitude prediction η₃ = |C (2, 2, 0) ³|/|C (2, 2, 0) |³ = n·fbulk = 1. 255×10⁻² is FALSIFIED by direct measurement on the public Dyer an attempted “all quadratics = n·fIII” generalization was tested and failed. The cubic mode’s existence and (6, 6) localization, the Fano quadratic selection rule, the retrograde-spin rule, and nₘax stand. See appended erratum + correction note. Pipeline validated against the known quadratic (2, 2, 0) ²→ (4, 4) ratio. Dyer 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.

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