Topological Resonance at the Earth–Sun Libration Nodes: A Mass-Free Kinematic Lock

Abstract/Summary:This paper presents a complete, mass-free topological classification of all five Earth-Sun libration points (L1 through L5) within the Universal Kochenov Framework (UKF). We demonstrate that orbital resonance can be fully described using pure kinematic addresses and geometric invariants, completely eliminating the need for gravitational masses, the gravitational constant G, or numerical force epures. Key Highlights: Two Topological Classes: The classical libration nodes are strictly segregated into Radial Nodes (L1, L2) and Phase Nodes (L3, L4, L5). The Volumetric Operator (μL=a3μL=a3): Radial saddle points compensate for orbital mismatch via a mass-free metric compression/decompression operator derived directly from the address geometry. Farey Phase Interference: The stable phase wells (L3, L4, L5) are localized at the base address a=1.00a=1.00 AU and are maintained in resonance exclusively via geometric interference governed by discrete Farey fractions (1/2, 1/6, 5/6). JWST Stability: The extreme stability and minimal fuel consumption of the James Webb Space Telescope at L2L2 are explained not by a fragile gravitational balance, but by topological localization within a macroscopic standing wave (a Farey cell). Empirical Confirmation: Using JPL Horizons geometric state vectors (Epoch 2026-Oct-24), the framework successfully confirms the 3D nature of the L2 region and links the lunar orbital inclination to the activation of the volumetric operator D(3)). Conclusion:The metric ignores mass. It obeys the address. This work reduces celestial mechanics to pure geometric invariants.