Theta Closure in Modal Triplet Theory III: Conditional Twistor–Action Matching and Normalization Audit

We audit a conditional Route B representation of the leading-order nonabelian overlap coefficients in Modal Triplet Theory using the self-dual Yang-Mills twistor corner. A standard SDYM twistor action is holomorphic BF-type; it does not by itself provide the positive Hermitian norm or relative coupling normalization used by Route A. We therefore isolate a reconstruction-and-norm bridge as an explicit assumption. The weak-sector comparison also uses a direction-sphere bridge and the effective round two-sphere lens model, while the color comparison uses the declared auxiliary nilmanifold, color harmonic, and factorization assumption of Paper II. Under these shared inputs Route B reproduces the two Route A overlap formulas. The result is a conditional dictionary check, not an independent derivation or selection of the overlap values and not a completed nonabelian Theta-closure theorem.