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Ellis Ye Yuan co-developed the scattering equations with Freddy Cachazo and Song He, connecting massless-particle kinematics with marked points on a sphere.^[ref] In a common convention,with conserved massless momenta $k_a$ and puncture coordinates ${\sigma }_a$. The equations provide algebraic structure for scattering calculations rather than trajectories of particles moving on that auxiliary sphere.

Freddy Cachazo co-developed the scattering equations with Song He and Ellis Ye Yuan. Their work connected kinematic invariants with punctures on a sphere and provided an inductive solution method, together with a proof of KLT orthogonality.^[ref]

The resulting auxiliary geometry organizes calculations of massless-particle scattering without treating that sphere as physical spacetime.

Song He, with Freddy Cachazo and Ellis Ye Yuan, established KLT orthogonality for objects built from solutions of the scattering equations. The orthogonality uses a specified bilinear form, not an arbitrary Euclidean inner product.^[ref]

This relates alternative organizations of particle-scattering data while keeping the momentum constraints explicit.