Kinematic variety for spinor brackets and multilinear rank

Show that the kinematic variety defined by spinor brackets of order ≤ 3 coincides with the variety of tensors whose multilinear rank is ≤ (2,4,2), as conjectured by Rajan–Sverrisdóttir–Sturmfels (Conjecture 6.2).

Background

Kinematic data for massless particles can be packaged in spinor brackets satisfying determinantal and rank constraints. The conjecture identifies this kinematic variety with a specified tensor-rank locus, bridging physics-inspired algebraic varieties with multilinear algebra. Proving the identification would unify representation-theoretic and tensorial descriptions of kinematics.