Extended Topological Quantum Field Theory (Part II): Admissible Morphisms, Spectral Embedding, and The Master Theorem of Stability

In the first paper of this series, we established the formal mathematical foundations of Extended Topological Quantum Field Theory (DFT-TQFT), introducing the categorical operators required to map infinite computational networks to invariant identity classes. This second paper provides the rigorous mathematical boundaries governing how these systems are permitted to evolve. We define the strict class of "Admissible Morphisms," proving that systemic transformations maintain topological identity, finite aggregation, and well-founded recursion if and only if they satisfy predefined mathematical constraints. Furthermore, we introduce Spectral Graph Embedding to ensure topological robustness via Ramanujan eigenvalue bounds, guarding against structural fragmentation. This paper culminates in the Synthesis Master Theorem, providing the definitive proof that systems adhering to these constraints remain unconditionally stable across infinite execution scaling.