This standalone paper presents the axiomatic resolution of the classical Three-Body Problem (TBP) within the Unified Field Theory-F (UFT-F) spectral framework. The resolution demonstrates that non-integrable, singular TBP solutions are physically inadmissible under the rigorous constraints of the Anti-Collision Identity (ACI). This stability is enforced by the Temporal Anti-Collision Constraint (TAC), derived from the ACI and the Time-Clock Continuum Hypothesis (TCCH). The core mechanism involves the Spectral Map $\Phi$, which links classical trajectories to a quantum-mechanical potential $V(x)$. Chaotic, singular orbits are excluded because they violate the $L^1$-Integrability Condition ($\mathbf{LIC}$), a spectral mandate for self-adjointness. Unconditional analytical closure is achieved via a categorical functor $\mathbf{F}: \mathbf{Mot} \to \mathbf{PhysSpec}$. The required existence of a strictly positive ground state eigenvalue ($\lambda_0 > 0$) is shown to be an axiomatic necessity, which provides an analytical foundation for quantum gravity singularity avoidance and resolves the observable matter-antimatter asymmetry. Computational validation via Python simulations confirms the exclusion of chaotic orbits, demonstrates $\mathbf{ACI}$ damping mechanisms, and provides $\mathbf{O(1)}$ complexity reductions. The work offers immediate practical applications in orbital mechanics, cosmology, and space debris mitigation (e.g., Kessler syndrome prevention through stable trajectory enforcement).