Classical gravitational scattering at high orders in Newton's constant G requires evaluating increasingly complex Feynman integrals. At O(G⁵) — five-loop order in the post-Minkowskian expansion — the integral families include Calabi-Yau geometries: the periods of the integrals satisfy differential equations whose solutions involve special functions associated with Calabi-Yau manifolds, not just polylogarithms or elliptic functions.
The paper shows that in the conservative sector — the part of the scattering amplitude that describes bound-state dynamics without radiation — the Calabi-Yau integrals cancel. They appear in individual diagrams but sum to zero in the physical observable. The conservative two-body dynamics at O(G⁵) involves only polylogarithmic and elliptic functions, despite individual contributions requiring Calabi-Yau periods.
The cancellation is structural, not numerical. The UV structure of the theory — obtained by examining the scattering amplitude at high energies — determines which integral topologies can contribute to the conservative sector. Calabi-Yau topologies are absent from the UV, and this UV absence propagates to the full amplitude through unitarity relations. The cancellation is visible before computing the integrals.
The result is a simplification that transcendence predicts: the mathematical complexity of the final answer is lower than the complexity of the intermediate steps. Individual Feynman diagrams probe geometric structures (Calabi-Yau manifolds) that the physical observable doesn't see. The geometry of the computation is richer than the geometry of the result — a recurring theme in amplitude methods, where symmetries hidden at the diagram level manifest as simplifications at the level of the full amplitude.