Computable Transformation of Five-Dimensional System Theory: Iterative Calibration and Verification of Orbital Synergy Coefficients in the Solar System

System science has long lacked a universal framework capable of describing diverse complex systems. Taking solar system orbits as a case study, this paper demonstrates the feasibility and operability of transforming five-dimensional system theory into a computable tool for celestial mechanics. Through iterative calibration of the reference frame, an "assignment--aggregation" orthogonal robustness test framework is constructed to verify the robustness and limitations of the synergy coefficient kappa, confirming that the essence of synergy is "five-dimensional complementarity" and that the product structure is the only faithful mathematical expression of the complementary synergy principle of five-dimensional system theory. Furthermore, inter-dimensional synergy coefficients are proposed as an internal self-check tool for the rationality of dimensional mapping rules, revealing that high synergy (>0.8) exposes redundant definition risks while moderate coupling (0.2~0.7) characterizes healthy dimensional relationships. This work provides an operational synergy quantification paradigm for systems science methodology.