Both eccentricities increase timing ranges in the tested TOI-4600 orbit

We test how both eccentricities affect transit times in a published orbit for TOI-4600 b and c. The input uses the printed marginal medians in Hu et al. (2026), Table 7, in Jacobi coordinates. This is one specified model orbit. It is not a joint posterior sample. We integrate Newtonian motion for 6,000 days and remove a separate linear ephemeris from each case and planet. The maximum minus minimum residual is 104.6 minutes for b and 126.9 minutes for c. A circular inner orbit reduces these ranges to 23.1 and 29.7 minutes. A circular outer orbit reduces them to 10.9 and 20.4 minutes. The same direction of change holds in 30 input sets, with one input changed at a time. An exact planar interaction calculation shows that the largest apsidal mode has the lowest factor e_b e_c^4. The circular outer timing signal has a separate geometric cause. Prescribed Jacobi Kepler orbits with no planet-planet forcing give a 9.27-minute outer semi-amplitude through stellar motion. Once sampled per outer orbit, this signal has the same nominal 2,954.93-day period as the near-6:1 combination. These mechanisms are known. Our contribution gives their sizes and numerical controls for this target. An independent direct-force solver and convergence tests check the calculation. A fresh run reproduces all numerical CSV files byte for byte in the same software environment. The package preserves code, input facts, source records, results, figures, and reproduction instructions. It contains no new observed transit times. The results do not give probability limits or transit scheduling uncertainties.

TOI-4600 · transit timing · eccentricity · Jacobi coordinates · stellar motion · sampling · orbital dynamics · reproducible calculation