A Computer-Assisted Exclusion Result for Signed Equilateral Triads in the Plane

We consider six planar sites with source strengths +1, +1, +1, -1, -1, -1, where the positive and negative triples are each constrained to form an equilateral triangle. The triangles may have different positive circumradii, arbitrary relative phase, and arbitrary relative translation. We prove that no collision-free configuration in this family makes the signed inverse-square field vanish at all six sites. The proof combines analytic bounds that place every hypothetical equilibrium in a compact parameter domain separated from collisions with a finite interval branch-and-bound certificate. The phase is rationalized by the half-angle substitution, and every interval operation in the certificate uses outward-rounded fixed-point integer arithmetic. Two certificates at distinct scales, 10^24 and 10^12, have been replayed with an independent rational-interval implementation; both cover the complete initial domain and exclude every terminal box. The conclusion is restricted to the two-equilateral-triad ansatz and does not imply non-existence for arbitrary six-point configurations or for general six-body choreographies. Source code, interval-arithmetic traces, and certificate replay scripts are included as supplementary files.