A G2-Symmetric Fano Lattice as a Geometric Model of Spacetime: Structure, Dynamics, and Falsifiable Predictions

We present a geometric model of spacetime in which the observable universe is a four- dimensional brane whose automorphism group is the exceptional Lie group G2. The central object is the Fano lattice — the unique projective plane PG(2, 2) on seven points encoding the multiplication table of the octonions O = H+ ⊕H−, where H+ and H−are the matter and colour quaternionic sectors. The root system of G2 possesses a degeneracy asymmetry: six long roots (length √ 3, small stabiliser, more degenerate) and six short roots (length 1, large stabiliser, less degenerate), with orbit-volume ratio D = 3 forced by the Cartan matrix. Its square root √ 3 is established as Geometric Prior #1 by showing it appears independently in the Cabibbo angle, the QCD coupling amplification, and the Fano truss geometry. Two further priors are established: 1/ √ 2 from H+ ,→O (Heisenberg bound, Kruskal normalisation), and 2π from the minimum holonomy period of G2/SO(4) (MOND scale, partition function periodicity). These three priors, each independently locked be- fore any entropy calculation, combine to yield the Bekenstein-Hawking coefficient exactly: sface = √ 2 · H7(a∗)/(2π √ 3) = √ 2 · π p 3/8/(2π √ 3) = 1/4. The same fixed-point cou- pling a∗= ln 3 simultaneously determines λCKM = 0.2248 (obs. 0.2252), the Koide ratio K = 2/3 (exact), ΩΛ = 0.685 (exact), and a0 = cH0/2π (MOND), all with one free pa- rameter (δM/M ≈6.1×10−10, the baryonic mass fraction set by the brane nucleation ini- tial conditions). Five falsifiable predictions are stated; one (CMB lensing √Feff = 0.9796) is confirmed by Planck 2018 with ∆χ2 = 10.14 and zero additional parameters. 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.