MAJORANT SERIES FOR THE N-BODY PROBLEM

Mikel Antoñana, Philippe Chartier, Ander Murua

correctmedium confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper rigorously constructs majorant series for the Newtonian N-body problem, proving a scalar majorant ODE in physical time (equation (20)) and deriving an explicit integral formula for the time-radius r(η0) via a first integral, as well as a uniform analyticity strip in the renormalized time τ with half-width R ≈ 0.0839968103939379 (Proposition 4) . The candidate solution reproduces the same main bounds and constants, including the same integral expressions and numerical value for R, though it sketches a somewhat different route (e.g., a Padé-type majorant and a v-variable), while the paper proceeds via coupled majorants (ξ, ζ) and an algebraic change of variables. The results and constants coincide, but some steps of the model differ from the paper’s derivation.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper offers a correct and essentially self-contained treatment of majorant series for the N-body problem, improving known analyticity bounds and delivering explicit constants. Its arguments are rigorous and the results are valuable for both analysis and numerics. Minor clarifications (especially around the algebraic reduction leading to Proposition 4) would further enhance readability. The candidate solution aligns with the paper’s results, differing only in some technical choices and presentation.