\begin{thebibliography}{99}

\bibitem{ACS12} A.~Albouy, H.~E.~Cabral and A.~A.~Santos, \emph{Some problems on the classical $N$-body problem}, Celest. Mech. Dyn. Astron. \textbf{113} (2012), 369--375.

\bibitem{AK12} A.~Albouy and V.~Kaloshin, \emph{Finiteness of central configurations of five bodies in the plane}, Ann. of Math. (2) \textbf{176} (2012), 535--588.

\bibitem{AM26} K.~Aquino-Michaels, \emph{Reducing the Chang--Chen residual: certified eliminations in the planar six-body central-configuration problem}, preprint (2026), \url{https://github.com/no-way-labs/smale6-residual}, commit \texttt{07f6c99}.

\bibitem{BES21} J.~Berthomieu, C.~Eder and M.~Safey El Din, \emph{msolve: a library for solving polynomial systems}, in: Proceedings of ISSAC 2021, ACM, 2021, 51--58.

\bibitem{CC23} K.-M.~Chang and K.-C.~Chen, \emph{Toward finiteness of central configurations for the planar six-body problem by symbolic computations}, arXiv:2303.02853 (2023).

\bibitem{CC24} K.-M.~Chang and K.-C.~Chen, \emph{Toward finiteness of central configurations for the planar six-body problem by symbolic computations. (I) Determine diagrams and orders}, J. Symbolic Comput. \textbf{123} (2024), 102277.

\bibitem{CC25} K.-M.~Chang and K.-C.~Chen, \emph{Toward finiteness of central configurations for the planar six-body problem by symbolic computations. (II) Determine mass relations}, SIAM J. Appl. Dyn. Syst. \textbf{24} (2025), 2369--2404.

\bibitem{CT26} Z.~Chen and Z.~Tong, \emph{Finiteness of planar central configurations of five bodies for all positive masses: On Smale's sixth problem}, arXiv:2610.16107 (2026).

\bibitem{DGPS} W.~Decker, G.-M.~Greuel, G.~Pfister and H.~Sch\"onemann, \emph{Singular 4.4.1 --- A computer algebra system for polynomial computations}, \url{https://www.singular.uni-kl.de}.

\bibitem{FLINT} The FLINT team, \emph{FLINT: Fast Library for Number Theory}, version 3.6.0, \url{https://flintlib.org}.

\bibitem{GS} D.~R.~Grayson and M.~E.~Stillman, \emph{Macaulay2, a software system for research in algebraic geometry}, version 1.25.11, \url{https://macaulay2.com}.

\bibitem{EGA2} A.~Grothendieck, \emph{\'El\'ements de g\'eom\'etrie alg\'ebrique II}, Publ. Math. IH\'ES \textbf{8} (1961).

\bibitem{HM06} M.~Hampton and R.~Moeckel, \emph{Finiteness of relative equilibria of the four-body problem}, Invent. Math. \textbf{163} (2006), 289--312.

\bibitem{HH18} Q.~Huangfu and J.~A.~J.~Hall, \emph{Parallelizing the dual revised simplex method}, Math. Program. Comput. \textbf{10} (2018), 119--142.

\bibitem{Jen} A.~N.~Jensen, \emph{Gfan, a software system for Gr\"obner fans and tropical varieties}, version 0.7.

\bibitem{JL25} A.~Jensen and A.~Leykin, \emph{Smale's 6th problem for generic masses}, J. Exp. Math. \textbf{1} (2025), 306--314.

\bibitem{Joh17} F.~Johansson, \emph{Arb: efficient arbitrary-precision midpoint-radius interval arithmetic}, IEEE Trans. Comput. \textbf{66} (2017), 1281--1292.

\bibitem{Jun04} U.~Junker, \emph{QuickXplain: preferred explanations and relaxations for over-constrained problems}, in: Proceedings of AAAI 2004, AAAI Press, 2004, 167--172.

\bibitem{Kra69} R.~Krawczyk, \emph{Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken}, Computing \textbf{4} (1969), 187--201.

\bibitem{SymPy} A.~Meurer et al., \emph{SymPy: symbolic computing in Python}, PeerJ Comput. Sci. \textbf{3} (2017), e103.

\bibitem{MZ19} M.~Moczurad and P.~Zgliczy\'nski, \emph{Central configurations in planar $n$-body problem for $n=5,6,7$ with equal masses}, Celest. Mech. Dyn. Astron. \textbf{131} (2019), 46.

\bibitem{MZ26} M.~Moczurad and P.~Zgliczy\'nski, \emph{Central configurations with unequal masses: finiteness in several exceptional cases of five bodies}, arXiv:2601.01165 (2026).

\bibitem{Moe14} R.~Moeckel, \emph{Lectures on central configurations}, lecture notes, 2014.

\bibitem{Mou10} F.~R.~Moulton, \emph{The straight line solutions of the problem of $n$ bodies}, Ann. of Math. (2) \textbf{12} (1910), 1--17.

\bibitem{Rob99} G.~E.~Roberts, \emph{A continuum of relative equilibria in the five-body problem}, Physica D \textbf{127} (1999), 141--145.

\bibitem{Sma98} S.~Smale, \emph{Mathematical problems for the next century}, Math. Intelligencer \textbf{20} (1998), no.~2, 7--15.

\bibitem{Tom26} T.~S.~Tomar, \emph{Smale's sixth problem for five bodies in the plane, with a proof formalized in Lean}, arXiv:2610.13100 (2026); version~1 is titled \emph{Finiteness of planar central configurations of five bodies for all positive masses}. Numbering as in version~2, \url{https://doi.org/10.5281/zenodo.23406010}.

\end{thebibliography}