Paper CLXII of the One-Octonion Brane-Bulk Series Luminous Fast Blue Optical Transients as Merging Dual Hyperbolic Infundibula: The Compact Object + Wolf-Rayet Binary as a G₂

Nugent et al. (2026, arXiv:2603.23597) present the largest uniform analysis of Luminous Fast Blue Optical Transient (LFBOT) host galaxies to date, concluding that hosts are "metal-poor" and proposing a compact object + Wolf-Rayet (WR) star merger progenitor. We argue, using the One-Octonion Brane-Bulk Framework, that (1) the host metallicity is not sub-solar but rather solar: the median Nugent et al. oxygen abundance 12+log(O/H) = 8.71 is 0.02 dex above the solar value of 8.69, and the apparent 'metal-poor' label arises from comparison to SN Ibc/II occurring in metal-enriched inner spirals; (2) the standard O/H metallicity proxy underestimates total metallicity because the isobaric Co→Ni channel (Paper CLIX, Jagadeesan 2026) enriches LFBOT environments in Fe-group elements by 10–20% beyond model predictions, producing a low O/Fe ratio at solar total metallicity; and (3) the compact object + WR star binary is precisely the dual hyperbolic infundibula system established in Paper CXLVIII (Cygnus X-1), scaled to LFBOT parameters. Both bodies have κ=−1 zones (r_a0 ≈ 8,000–33,000 AU) vastly exceeding the binary orbital separation (≤0.1 AU), so the entire system is embedded in the dual κ=−1 regime throughout its lifetime. The LFBOT event itself is the coalescence of two overlapping G₂ permutohedra, with the H sector ⁺ (8 hexagonal faces) producing the fast blue optical emission and the H sector (6 square faces) producing ⁻ the X-ray/jet component. Three predictions follow: the O/Fe ratio in LFBOT ejecta is anomalously low (same isobaric channel as Paper CLIX); the optical-to-X-ray luminosity ratio is 8/6 (from G₂ ∼ permutohedron face geometry, qualitative); and LFBOTs should occur at solar total metallicity independent of gas-phase O/H. 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.