The G₂ Fano Lattice as the Origin of the Auxetic Brane Properties: c(t) H(t), ħ(t) H(t)³, and a₀ = cH₀/2π We show that the G₂-symmetric Fano lattice, arising as the automorphism group of the single

We show that the G₂-symmetric Fano lattice, arising as the automorphism group of the single octonion O = H H , forces the brane to be an auxetic material with Poisson ratio ν = −1. This ⁺ ⊕ ⁻ auxetic property has two immediate and exact consequences for the physical constants c and H: (i) the brane acoustic speed (speed of light) is c(t) = c₀ H(t)/H₀, making c proportional to the Hubble expansion rate H; and (ii) the Planck constant satisfies ħ(t) H(t)³, because ħ = ℓ_P m_P c and ℓ_P ∝ is fixed by the Planck length being constant. Both c(t) and ħ(t) are auxetic properties of the Fano truss, not postulates. Their ratio α = e²/(ħc) = const: the fine structure constant is conserved exactly. The MOND acceleration scale a₀ = cH₀/2π = 1.043×10 ¹ m/s² follows from the zero-jerk ⁻ ⁰ condition on the sump geodesic and requires no free parameter. The CMB hemispherical asymmetry A_hemi = 2√3/49 = 7.07% is derived from the G₂ root structure. The Carreau-Yasuda brane rheology ᵥ(a) = [1+(a/a₀)²](n−1)/4 with n = 0.34 is predicted as the brane's shear-thinning response to acceleration gradients. All three predictions carry zero free parameters. 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.