Preprint of a manuscript submitted to Nonlinearity. We prove a computer-assisted threshold comparison theorem for invariant circles in the standard-sine conservative twist map. For a fixed threshold branch, a fixed normalization of rotation classes, and a finite generated comparison domain, we certify that the golden rotation class has the largest threshold among the generated classes. The final theorem is the outward-rounded endpoint comparison U^+_ng = 0.9716347 < 0.9716350 = K^-_G. The result is not a proof of Greene's conjecture over all irrational rotation numbers and is not a universality theorem for arbitrary twist maps. The associated proof package, theorem-facing artifacts, replay scripts, and verification records are available at DOI: 10.5281/zenodo.20101820.