Dimension-Independent Finiteness of Central Configurations for Positive Masses

Key Points

• This work addresses the number of central configurations for positive masses in higher dimensions, specifically proving their finiteness.
• Proved finite central configurations modulo similarity for N ≥ 3 bodies in d dimensions (d ≥ 2).
• Utilized formal verification tools, including Lean 4 and Python verification scripts.
• Part of the broader Latent research program encompassing related studies.
• Demonstrated that the number of central configurations is finite for bodies with positive masses in all dimensions d ≥ 2.
• Resolved Smale's 6th Problem by showing this finiteness holds universally across specified dimensions.