Graviton scattering in the brane-bulk octonionic framework is derived from rst principles of Fano lattice mechanics. A graviton is identied as a transverse-traceless (TT) shear wave propagating along the brane a spin-2 mode in the j = 2 irreducible representation of G2, carrying no rest mass (δH = 0, Paper III) and coupling univer- sally to all focal deceleration zones through the sump mechanism. Newton's constant G is the brane-bulk interface transmission coecient (Paper XVI); the graviton coupling κ = √ 32πG is zero-parameter it is xed by the Fano lattice stiness k ∝H(t)2 (Paper XXV). The auxetic Poisson ratio ν = −1 mechanically eliminates longitudinal polarisation modes at each vertex: the boundary terms ∝|1 + ν| in the vertex ampli- tude (Paper LXXVIII) vanish exactly, leaving only TT modes as physical propagating degrees of freedom. Tree-level graviton scattering therefore agrees exactly with general relativity on all physical (TT) polarisation states, without gauge xing dieomor- phism invariance is derived as a consequence of Fano automorphism invariance rather than postulated. Loop corrections are UV nite: the Fano lattice has a hard maximum spatial frequency kmax = π/ℓP , providing a physical regulator. The one-loop graviton self-energy is: ΠFano(0) = C2(G2) κ2π4 (4π)2ℓ4 P = 4 × κ2π4 (4π)2ℓ4 P where C2(G2) = 4 is the Casimir eigenvalue of the fundamental G2 representation a calculable, framework-native coecient. Low-energy corrections to gravitational am- plitudes are suppressed by (k/kmax)2 = (ℓP k/π)2, undetectable at current scales but structurally distinct from GR. Four new predictions are made (P37P40). 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 (Fri,) studied this question.