A computer assisted proof for 100,000 years stability of the solar system

The paper claims a computer-assisted proof that, for the Sun + 8 planets + Pluto with J2000 uncertainties (±1e−4 in elements and masses, except ±10% for Mercury/Mars/Pluto masses), all semi-major axes vary by at most 1% and eccentricities/inclinations remain bounded over 100,000 years. However, (i) the stated theorem relies essentially on non-validated numerics: a 4-step Adams–Bashforth integration on orbital-element ODEs with truncated series for x,y,z, ad hoc per-step error bounds, and an a posteriori “fundamental solution” estimate derived from additional numerical runs, none of which use interval arithmetic or produce rigorous enclosure bounds (see the theorem and method outline, the ODE system in elements, the truncated expansions, and the numerical scheme and error accumulation arguments ). (ii) The key stability constant ‖Φ(t)−I‖<1/5 is justified only by further floating-point integrations and finite-difference sensitivities, not by a rigorous bound with controlled rounding/truncation errors (see their construction of Φ and bound statement ). (iii) The paper’s own numerical Table 1 shows semi-major-axis excursions exceeding 1% for Uranus and Neptune over 10^5 years, contradicting the headline 1% theorem (e.g., Neptune 29.766–30.247 AU, a >1.6% span; Pluto even larger), undercutting the central claim even at the level of the reported computation . By contrast, the model’s assessment that a fully rigorous, uniform proof at real masses for the full 3D Sun+9 system and the specified uncertainty box was likely open as of 2022-06-27 aligns with the contemporary literature on KAM/Nekhoroshev theory for planetary problems and its quantitative limitations.