The Two-Sector Brane-Bulk CMB: G2 ⊃SU(3) Bifurcation at H⋆, ERB Boundary Cur- rent, Corrected S8 Projection, and Scale-Dependent CMB Rotation Paper LXXXIV of the Brane-Bulk Octonionic Series

At H = H⋆= √H0Hrec = 10, 634 km/s/Mpc the brane eld decomposes under the group chain G2 ⊃SU (3) into two sectors: an isotropic sector (G2-symmetric, k = 0, partition function Ziso = 27 = 128) that reproduces ΛCDM at leading order, and an anisotropic sector (G2/SU (3) ∼= S6, k ̸= 0, Zaniso = (1 + T) 6|1 −2T| = 97. 90) that generates all departures from ΛCDM at order sin θG2 ∼7%. We derive As = Ziso/Zaniso × (H0/H⋆) 4 = 2. 101 × 10−9 as the ratio of Fano Laplacian determinants; Ωb = sin θG2/ √ 2 as the U (1) B Noether current through the unique cross-sector Fano line 3, 4, 7; and the corrected S8, lens via the full Fano-line coherent projection, recover- ing S8, lens = 0. 8146 (KiDS-Legacy 2025: 0. 815 ± 0. 018, 0. 001σ residual). Classical uid perturbation theory recovers only the rigid p 6/7 limit; the additional 3 √ 2 sin θ correc- tion arises from o-diagonal coherent cross-terms in the Fano multiplication table that are invisible to any classical uid treatment. The G2 tilt generates a scale-dependent rotation δϕ (ℓ) = (θG2/N⋆) ln (ℓ/ℓ⋆) predicting 4◦total rotation from ℓ= 2 to ℓ= 220, explaining the quadrupole-octopole alignment anomaly. We additionally show that the Fano lattice cannot tile at 4D spacetime without defects; the auxetic constraint ν = −1 forbids bare gaps; the resolution is persistent shear (the UMa tidal eld) plus G2 →F4 nodal reordering at H⋆; and the geometrically suppressed e7 mode is the irreducible topological remainder of this process. 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.