We test the Θ-closure program of Modal Triplet Theory (MTT) by imposing a redundant constraint entirely within the Standard Model gauge sector. In earlier work, a single parameter Θ was fixed using the nonabelian gauge coupling ratios at a common matching scale. Here we ask whether the same Θ, without retuning or additional free parameters, also reproduces the observed value of the weak mixing angle sin2θW²Wsin2θW. Using one-loop renormalization group evolution with canonical hypercharge normalization, we derive a predicted sin2θW (MZ) ²W (MZ) sin2θW (MZ) from the Θ-fixed gauge couplings. We carefully distinguish between a round-trip consistency check and a genuinely non-circular redundancy test, fixing only one unavoidable normalization and using Θ-fixed overlap ratios to determine the remaining couplings. The resulting prediction agrees with experiment within the expected theoretical uncertainty of the one-loop approximation. This demonstrates that the Standard Model gauge sector is overconstrained within the Θ-closure framework and provides a sharp internal consistency test with clear falsification criteria.
Peter Nero (Thu,) studied this question.