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 $\bar{Q}^\Phi$ introduced in the fermion generations analysis [ref] are real traceless symmetric $3 \times 3$ matrices, spanning a 5-dimensional space $\Sym(3)$. The $\nu$-field rotations from the Layer-1 gauge enrichment [ref] generate the 3-dimensional Lie algebra $\so(3)$ of antisymmetric matrices. We prove that the direct sum $\so(3) \oplus \Sym(3)$ satisfies the three bracket conditions of a Cartan decomposition: $[\so(3), \so(3)] \subseteq \so(3)$, $[\so(3), \Sym(3)] \subseteq \Sym(3)$, and $[\Sym(3), \Sym(3)] \subseteq \so(3)$. The resulting 8-dimensional Lie algebra is $\mathfrak{sl}(3, \R)$, whose complexification $\mathfrak{sl}(3, \mathbb{C})$ admits three real forms: $\mathfrak{sl}(3,\R)$ (split), $\su(3)$ (compact), and $\su(2,1)$ (indefinite); the Cartan decomposition with $\mathfrak{k} = \so(3)$ excludes the third. The associated symmetric space is $\mathrm{SL}(3,\R)/\mathrm{SO}(3)$, whose compact dual is $\mathrm{SU}(3)/\mathrm{SO}(3)$ (Cartan type AI, rank 2). We argue that the LUFT stability axiom $I[\Phi] \geq 0$ provides a physical mechanism for selecting the compact form, though this step remains a conjecture. If confirmed, the same $\dim M = 3$ that produces three fermion generations also produces the $\mathfrak{sl}(3,\R)$ color algebra whose compact dual is $\su(3)$---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.