Universal Apophatic Roots in Modal-Paraconsistent Multiverses

We prove that any non-trivial rooted S4 modal multiverse containing Gödel-undecidable branching forces a paraconsistent logic at its unique root. An explicit glutty apophatic object is constructed via diagonalization in every such model. In the associated indexed categorical semantics, every classical object is shown to arise as an epimorphic image of this single contradictory initial object via coherence functors. These results establish that paraconsistent semantics at foundational origins is not a metaphysical choice but a mathematical necessity for coherent modal-semantic treatments of Gödel-divergent classical theories under rooted Kripke frameworks. This work situates Gödel incompleteness as an architectural constraint on semantic unification, rather than a merely limitative theorem.