Collapse of the Compositional Boundary and Direct Sum Decomposition under Strong Two-Type Quotients

This note proves that under the Strong Two-Type hypothesis, the compositional tracking operation collapses from the boundary and is uniquely determined as addition modulo 2. 

We establish a direct sum decomposition V ≅ H ⊕ Z₂ and show that the undecidable locus reduces to the boundary core {ε = f(K), S-type}. 

Furthermore, admissible kernel extensions are completely classified into three mutually exclusive structural classes.