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 = ℓP mP c and ℓP ∝ 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 Aₕemi = 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.