We derive the cosmological constant ρΛ from first principles via two independent, zero-free- parameter routes grounded in the One-Octonion Brane-Bulk framework. The starting point is that the matter–antimatter asymmetry δM/M = 6. 10×10 ¹ (Paper CLX) produces exactly one ⁻ ⁰ unpaired e₇ lattice node per baryon. Each e₇ node is frozen — left-handed, color-singlet, unable to annihilate — because e₄, e₅, e₆ = −2e₇ algebraically forbids a partner. These frozen nodes constitute a spatially isotropic, Lorentzian lattice whose causal geometry derives the metric signature (−, +, +, +) and whose isotropy forces w = −1, both without free parameters. Route A (top-down, Papers XLII + G₂ mode selection): The Fano zero-point vacuum energy is ρΛ (XLII) = ħH₀²/ (ℓP²c). Of the 14 G₂ generators, only e₇ is frozen; the other 13 cancel through H /H pairing. This gives ρΛ = ħH₀²/ (14ℓP²c) = 4. 589×10 ¹ J/m³, which is 87. 4% of the ⁺ ⁻ ⁻ ⁰ observed value. Route B (bottom-up, e₇ node counting): Each frozen node carries vacuum energy Eγ = 19. 51 GeV (Paper CLXXIX, G₂-curved transit). The node density is nb = δM/M × n_γ = 0. 2505 m ³. ⁻ The spatial Lorentzian fraction 3/4 and sump frozen fraction fₛump = exp (−t/Tₛump) = 0. 827 give ρΛ = (3/4) × nb × fₛump × Eγ = 4. 859×10 ¹ J/m³, which is 92. 5% of the observed value. ⁻ ⁰ The two routes agree with each other to 5. 6% and with observation to 7. 5–12. 6%. The residual gap is within the theoretical uncertainty of the framework parameters. Both routes bracket the observed ρΛ = 5. 251×10 ¹ J/m³ from below with zero free parameters. ⁻ ⁰ 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.
Bharathi Jagadeesan (Sat,) studied this question.