Paper LXXXIV: 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

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.