The optimal Hessian bound for convex four-body central configurations
A Lean 4 and Mathlib formalization of Conjecture 7.3 of arXiv:2609.35632 on the central configurations of the planar Newtonian four-body problem. At every strictly convex central configuration of four positive masses, the Hessian form Q of U + (λ/2)I is at least two thirds of its radial part K, and strictly so wherever K is positive. In the notation of the paper this is λ_max(G) < 1/3 for the explicit 2×2 matrix G of its Proposition 3.5, and by its Proposition 7.2 the constant 2/3 is optimal. It sharpens Theorem B of the paper, Q ≥ K/4. The definitions and the reduction to the normal form of…
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