Paper CXXXVIII: The Permutohedron Form κ = −1 Brane Transition, Perpetuated Asymmetric Mass Creation, and the

We derive the S8 tension between Planck CMB and KiDS-1000 weak-lensing measure- ments exactly from first principles in the G2-brane framework. The κ = −1 global curvature transition of the brane (Hyperbolic Necessity, Paper CXXIX) does not oc- cur isotropically: it takes the form of a permutohedron with negative curvature in 4-dimensional spacetime. The permutohedron of order 4 has 4! = 24 vertices un- der the full S4 permutation group, but with one direction fixed by the Ursa Major twist (τ = arccos(1/ √ 7), the primary boundary condition), the stabilizer is S3 with |S3| = 3! = 6 elements, giving 4!/3! = 4 coset sectors of unequal mass density. The twist (not the tilt) contributes the dominant asymmetry: sin τ = p 6/7 and cos τ = 1/ √ 7 encode the projection of the 7-dimensional G2 octonion structure onto the 4D brane. The cross-term between the aligned (S3) and asymmetric (18-element) sectors gives a matter power suppression that is perpetuated through all subsequent structure for- mation because the permutohedron geometry is topologically fixed at the κ = −1 transition, not dynamically generated. The result is: δS8 S8 = sin τ cos τ 4!/3! = √ 6/7 4 = √ 6 28 = 8.748%, 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.