Verified Hill region topology and parameter sensitivity in the Sun–Jupiter restricted three body problem

Background and objective: Lagrange points and forbidden regions in the circular restricted three body problem are classical, but comparisons between published Sun–Jupiter calculations can be obscured by different mass parameters and additive conventions for the Jacobi constant. We investigate whether these historical differences change the ordering of the critical thresholds, and provide independently checked numerical benchmarks. Methods: Five published parameterizations define a historical model envelope, not a physical uncertainty interval. Directed decimal interval arithmetic encloses the collinear equilibria throughout that envelope; exact rational interval arithmetic checks the reported bounds. We also compare two Jacobi conventions, correct a planar periodic orbit near the first collinear point, and measure oscillation frequencies near a triangular point over more than ten slow cycles. Results: The three successive critical gaps remain strictly greater than 0.00127185, 0.0365307, and 0.00190647 throughout the envelope. The collinear coordinates vary monotonically, and the triangular points remain spectrally stable. Historical parameter choices shift the first collinear coordinate by approximately 3349 km under a fixed nominal scale, whereas differences among the examined JPL solutions are below one kilometer. The corrected orbit and independent integration checks provide additional reproducibility targets. Conclusions: The contribution is a parameter-uniform certificate and a quantified historical comparison, not a new equilibrium theory. The threshold sequence is robust within the stated circular model. Omitted eccentricity produces a much larger dimensional scale variation, so numerical agreement must not be interpreted as physical prediction accuracy. Kaiwei Wang, Mingquan Luo, and Yuan Yao are co-first authors of this manuscript.