Algebraic Origin of Color Structure from Three-Dimensional Geometry

We exhibit an algebraic structure underlying color symmetry that arises from mathematical objects already present in Lambda Convergence Universal Field Theory (LUFT). The shape tensors Q̄^Φ introduced in the fermion generations analysis [ref] are real traceless symmetric 3 × 3 matrices, spanning a 5-dimensional space (3). The ν-field rotations from the Layer-1 gauge enrichment [ref] generate the 3-dimensional Lie algebra (3) of antisymmetric matrices. We prove that the direct sum (3) ⊕ (3) satisfies the three bracket conditions of a Cartan decomposition: [(3), (3)] ⊆ (3), [(3), (3)] ⊆ (3), and [(3), (3)] ⊆ (3). The resulting 8-dimensional Lie algebra is sl(3, ), whose complexification sl(3, C) admits three real forms: sl(3,) (split), (3) (compact), and (2,1) (indefinite); the Cartan decomposition with k = (3) excludes the third. The associated symmetric space is SL(3,)/SO(3), whose compact dual is SU(3)/SO(3) (Cartan type AI, rank 2). We argue that the LUFT stability axiom I[Φ] ≥ 0 provides a physical mechanism for selecting the compact form, though this step remains a conjecture. If confirmed, the same M = 3 that produces three fermion generations also produces the sl(3,) color algebra whose compact dual is (3)---without postulating non-Abelian gauge groups. Physical implications including color identification, a confinement mechanism, and open problems are discussed with explicit status markers. Version note (v1.4.0, July 2026): A/B-sync with the spine v2.13.0 retraction: all c2 = A/B statements are replaced — A/B is a quadrature ratio with no kinematic content; the propagation cone is carried by the dispersion route (c2 = alpha*kappa at tree level, conditional on OS reconstruction). The earlier "time emerges from c2 = A/B" phrasing is replaced (time is emergent via the relational Xi-monotone). Terminology: LUFT = Lambda Convergence Universal Field Theory. Algebraic content unchanged.