Collapse of the Shared Preservation Structure and Dynamic Bridging: Does the Interface Between Locally Solvable Modules Regenerate an Existential Quantifier?

Split the overall problem into local modules F_i(B_i,Y_i); each module first eliminates its private variables Y_i, keeping only a Boundary Extension Relation E_i(B_i) — but global satisfiability is exactly equivalent to ∃B ∀i, b|B_i∈E_i. Once the private existential quantifiers are eliminated, a global existential quantifier reappears on the shared boundary — called “Existential Quantifier Reappearance.” The cleanest counterexample treats every clause as its own independent module: local decision costs are nearly constant, but if the bridge could coordinate all the clauses in polynomial time, it would already be a general SAT solver — the Bridging Universality Trap. The Equals Team immediately counters with real precedents: Nelson-Oppen theory combination, DPLL(T), and the 2026 CDCL(⊕) all demonstrate that distinct local algebras genuinely can cooperate through a bridging layer, without needing to share the same polymorphism. Establishes five working objects: the Boundary Extension Relation, Existential Quantifier Reappearance, the Polynomial Bridging Principle, the Bridging Universality Trap, and Bridging Coordination Debt.