Bharathi Jagadeesan
A rival has arrived on the unitarity triangle, and the confrontation is unusually clean. Arkani-Hamed, Figueiredo, Hall and Manzari (AHFHM, arXiv:2607.27315) observe that the CKM unitarity-triangle angles lie close to simple fractions of π — (α, β, γ) ≈ (π/2, π/8, 3π/8) — and propose sparse “9-link” Yukawa textures with a spontaneously broken CP phase quantized in multiples of π/8. This note shows the One-Octonion Brane-Bulk (OOB) framework already contains the pattern, with a different and sharper origin. (i) The flat OOB triangle is exactly right-angled. With apex (ρ̅, η̅) = (1/7, √6/7) fixed by the √7 Dehn twist, the apex sides are exactly orthogonal (−6/49 + 6/49 = 0): αflat = π/2 identically, with the right angle split as tan γflat = √6, so γflat = arccos(1/√7) = 67.79° = 3π/8 + 0.29°. The proximity to the π/8 lattice needs no discrete symmetry: an irrational Gudermannian angle grazes it. (ii) One bulk-transit depth warps the observed triangle. α0 = 0.10673 gives (α, β, γ) = (92.01°, 22.63°, 65.36°) — each within 0.4σ of PDG 2026, in a statistical dead heat with the AHFHM anchors today. (iii) The texture-level cross-match. Written in AHFHM's own parametrization (up-frame diagonal; down sector sparsified with the right-handed U(3)dR freedom to a canonical RQ chart), the OOB flavor point lands exactly on their 3π/8-family texture #29 — identical zero pattern and phase slot Yd12 — as its canonical hierarchical representative. The single rephasing invariant is φ = 65.409° = γ + 0.045°: it tracks γ exactly as their leading-order theorem requires, with the next-order texture correction computed here. The same texture chart thus carries two incompatible phase laws: AHFHM-quantized #29 predicts γ ≈ 3π/8 − 0.045° = 67.455°; OOB predicts γ = 65.364°. The mirrored (lower-triangular) gauge reproduces AHFHM's anomalous π/4 histogram peak. Next-generation LHCb/Belle II determinations of γ (sub-degree, 2030s) decide. Framing (stated honestly): the texture identification is a canonical-coordinate statement — the RQ chart's loop phase is a determined, rephasing-invariant function of YdYd† — not a dynamical derivation of the texture; the group-theoretic (Ursa-Major S4 Clebsch-Gordan) route to the magnitudes remains open. No new parameter and no new prediction number is introduced; the note sharpens the framework's long-standing γ stake (Papers CXLIX, CCCII, CCCIII) to the texture level. Verification: one Python gate script and 19 independent Wolfram gates (including symbolic proofs of the exact right angle and tan γ = √6), all passing (supplementary files); one Fugu cross-model pre-publication audit with all confirmed findings repaired. The results are strictly contingent on the established OOB framework — the G2 = Aut(O) reduction, the √7 Ursa-Major twist and apex closure, the Wolfenstein closures λ = √3/(ea*+6) and A = 8/π2, and the Class-I transit depth α0 — none of which is re-derived here. Full symbolic proofs and postulates are consolidated in the BraneBulk Omnibus (concept DOI 10.5281/zenodo.19185171).