The three-body problem is famously chaotic. But proving that chaos is structurally robust — that it persists under perturbation and doesn't depend on special parameter values — requires more than numerical evidence. It requires constructing specific geometric objects in phase space.
Berger and Bounemoura (arXiv:2512.02133) construct symplectic blenders for both the restricted and full three-body problem. A blender is a hyperbolic invariant set whose stable and unstable manifolds overlap in a robust way — “robust” meaning the overlap survives perturbation. The consequence is a strong form of topological instability: nearby orbits can be pushed to arbitrarily different energies by small perturbations. This is Arnold diffusion in a concrete, constructive form.
The striking aspect: no smallness assumptions on the masses. Previous instability results for the three-body problem typically required one mass to be negligible (the restricted problem) or all perturbations to be small. Here, the only requirement is that at least two of the three masses are distinct. The construction works for the full gravitational problem at finite mass ratios.
The through-claim: the three-body problem isn't just numerically chaotic — it's provably, structurally unstable in the strongest possible sense, and this instability doesn't depend on asymptotic limits. The blender construction converts a physical intuition (three bodies are unpredictable) into a mathematical object (symplectic blender) that makes the instability formally robust.