A zero-fitting analytic comparison of the One-Octonion Brane-Bulk (OOB) derivation of the Koide relation against the recent J3(𝕒ℂ) construction of Teli & Singh (arXiv:2605.24866). OOB derives the charged-lepton Koide quantity K = 2/3 exactly from the ℤ3 Weyl orbit of the G2 short-root system (Papers CLXXXVI, CCII), G2 = Aut(𝕒) being the automorphism group of the very octonions whose 3×3 Hermitian algebra is J3(𝕒).
Four results. (1) The Teli–Singh arithmetic spectrum (q−δ, q, q+δ) with δ² = 3/8 yields Q(q) = 1/3 + 1/(12q²), which for physical (positive) eigenvalues is bounded above by Q_max = 5/9 ≈ 0.556 — it cannot by itself reach 2/3; their Koide value, like OOB's, must enter through a separate order-3 symmetry, not the mass ladder. (2) Both frameworks therefore share an identical algebraic root cause: the ℤ3 symmetry of the exceptional structure (G2 short-root 120° in OOB; the outer ℤ3 automorphism permuting the J3(𝕒) corners in Teli–Singh). (3) An independent recomputation of the lepton Koide phase (δ ≈ 132.7°) is identical to the OOB canonical angle δ = (2/3)π·α0 = 12.808° shifted by exactly the 120° G2 short-root step — one underlying phase, two ℤ3 conventions. (4) The genuinely new, distinguishing content of the Teli–Singh program is the ℤ2 (Dynkin) relation √(mτ/mμ) = √(ms/md), which is 8.3% discrepant at μ = 2 GeV and constitutes a clean falsifiable test once run to the unification scale. The up-type quark Koide (Q = 0.849) further shows the arithmetic ladder does not extend universally. Nothing in the comparison challenges any OOB canonical value; the external J3(𝕒) result independently corroborates the OOB Koide theorem.
Method note: physical framing and the OOB canonical results are the author's; the comparative algebra, the Q(q) bound, the phase reconciliation and all numerical checks were carried out collaboratively with Claude (Anthropic) at the author's direction and are reproduced by verify_teli_singh_koide_2026_06_17.py (all checks pass). The δ² = 3/8 step attributed to Teli & Singh is drawn from the abstract and indexed excerpts; their full text was inaccessible (HTTP 403) at the time of writing and that derivation is flagged in the paper as provisional.
Publication Date: 2026-06-17