Paper CCVIII: G2-Holonomy Riemannian Geometry and Baker-Campbell-Hausdorff Discretization as a Division-Algebra-Free Formulation :

The One-Octonion Brane-Bulk Framework has been presented using the octonion division algebra O = H+ ⊕H−as its primary language. We show that the framework is equivalent to the spectral theory of G2-holonomy Riemannian manifolds, and that all structural results — the Klein ladder mass eigenvalue spectrum, the hyperbolic brane curvature κ = −1, the 12-fold dihedral symmetry predictions, the brane-bulk transit fraction fbulk = 1−sinc2 (x), the nuclear surface diffuseness a = 0. 5453 ℏc/ΛQCD, and the three universal transit classes — follow from Riemannian geometry and Baker-Campbell-Hausdorff (BCH) discretization on the G2 root system, with zero reference to division algebra multiplication tables. The central objects are: (1) the G2 permutohedron Laplacian, whose six eigenvalues λk = 2 −2 cos (πk/6) for k = 1,. . . , 6 are the Klein ladder rungs; (2) BCH composition of adjacent Weyl reflections on g2, whose second-order correction produces the sinc2 transit suppression; and (3) the arithmetic hyper- bolic surface PSL (2, 7) 2, whose inradius gives the Woods-Saxon diffuseness and whose spectral gap λ1 = 1/4 gives the universal Class II transit fraction fbulk (II) = 1 −8/π2 = 18. 943%. We identify a new result: the Class II universal constant x = 1/4 is the Ramanujan spectral gap of the Klein Quartic arithmetic surface, establishing that the nuclear diffuseness and the Higgs decay width are controlled by the same arithmetic hyperbolic manifold. The complete framework requires one 1 dimensionless physical input (mµ/mπ = 0. 7569) and two dimensional scales (ΛQCD, H0). The division algebra is a computational shortcut, not a foundational requirement. 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.